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Terrestrial magnetism
and atmospheric electricity
Louis Agricola Bauer, John Adam Fleming
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TERRESTRIAL MAGNETISM
*H0
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Terrestrial Magnetism
An International Quarterly Journal
Edited and Published by
L. A. BAUER AND THOMAS FRENCH, Jr.
With the Cooperation of Eminent Magneticians
"Magnus magnes ipse est globus terrestris "
—Gilbert, ** De Magnete," 1600.
VOLUME III
MARCH-DECEMBER, 1898
The Editors
CINCINNATI, OHIO
The University op Cincinnati
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> >7<)
T . ".EN FOUNDAT
H 1900.
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CONTRIBUTORS TO VOLUME HI
Cleveland Abbe Washington, District of Columbia
Albert, Prince of Monaco
W. E. Ayrton London, England
L. A. Bauer Cincinnati, Ohio
W. van Bemmelen Batavia, Java
W. von Bezold Berlin, Germany
J. C. de Brito Capello Lisbon, Portugal
J. E. Davies Madison, Wisconsin
J. ELSTER ... Wolfenbiittel, Germany
M. Eschbnhagen Potsdam, Germany
H. Geitel Wolfenbiittel, Germany
J. F. Hayford Washington, District of Columbia
S. Lemstrom Helsingfors, Finland
G. W. Littlehales Washington, District of Columbia
E. Mascart Paris, France
Th. Moureaux Paris, France
G. R. Putnam Washington', District of Columbia
A. W. Rucker London, England
M. Rykatschew St Petersburg, Russia
Adolf Schmidt .... Gotha, Germany
Charles A. Schott Washington, District of Columbia
Arthur Schuster Manchester, England
R. F. Stupart Toronto, Canada
Paul Wernicke Lexington, Kentucky
E. J. Wilczynski Berkeley, California
v
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TABLE OF CONTENTS
GENERAL
PAGE
i.arth Currents, Atmospheric Currents and Magnetic Per-
turbations S. Lemstrom 128
Erdmagnetische Observatorien und Elbctrische Bahnen
M. Eschenhagen 83
Establishment of Temporary Magnetic Observatories
IV. von Bezold and M. Rykatschew 1 10
Expression of the Earth's Magnetic Potential . A. Schuster 124
Interpretation of Earth Current Observations . A. Schuster 130
LE NOUVEAU PAVILLON MAGNimQUB DE L'OBSBRVATOIRE DU PARC
St. Maur ••.... Th. Moureaux 1
Magnetic and Electrolytic Actions of Electric Railways 131
Magnetic Observations in the Azores
Albert, Prince of Monaco 1 19
MOUVEMENT DlURNE DU P6LE NORD D'UN BARREAU MAGNisTlQUE
/. B. Cape I to 120
Note in Regard to Magnetic Disturbances on St. George
Island, Bering Sea G. R. Putnam 44
On the Investigation of Hidden Periodicities with Applica-
tion to a Supposed Twenty-six-day Period of Meteoro-
logical Phenomena A. Schuster 13
Opening Address, International Conference on Terrestrial
Magnetism and Atmospheric Electricity . A. W. Rucker 99
Questions to be Addressed to Magnetic Observatories
M. Eschenhagen 116
Relative Advantages of Long and Short Magnets
E. Mascart 1 14
Report of the Permanent Committee on Terrestrial Mag-
netism and Atmospheric Electricity to the Interna-
tional Meteorological Conference . . . A. W. Ru\ ker 139
Results of Professor Eschenhagen's Magnetic Investiga-
tions in the Harz Mountains G*. R. Putnam 77
Systematische Erforschung der Saecular Variation
A. Schmidt (Gotha) 117
The Altitude of the Aurora above the Earth's Surface
C. Abbe 5, 53, 149
The International Conference on Terrestrial Magnetism
and Atmospheric Electricity 93
The Relation of Terrestrial Magnetism to Geology
A. W. Rucker 42
The Toronto Magnetic Observatory R. F. Stupart 145
vi
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TABLE OF CONTENTS vii
PAGE
Ueber eine Methods die Richtung Electrischbr Vertical-
strome in der atmosphaere durcu luftblbctrischb
BeobachTungbn zu Bestimmen. . ./. Elster and H. Geitel 9
Welcoming Address, International Conference on Terres-
trial Magnetism and Atmospheric Electricity
W. E. Ayrton 97
LETTERS TO EDITOR
Elementary Magnetic Waves C. Abbe 135
International Magnetic Conference 87
Mean Magnetic Elements for Year 1897 at Observatory Infant D. Luiz
(Lisbon) J.C.deB. Capello 87
Neue Beitrage zur Sammlung alterer Abweichungs-Beobachtungen
W. van Bemmelen 45
Photographic Reproductions of Plate9 in Lamont's Handbuch des
Erdmagnetismus M. Eschenhagen 87
United States Hydrographic Office Magnetic Variation and Dip Chart
for 1900 G. W. Littlehales 87
NOTES
Announcement of "Journal," Terrestrial Magnetism and Atmospheric
Electricity 194
Course in Terrestrial Magnetism at the University of Cincinnati . . 137
Course in Terrestrial Magnetism at the University of Wisconsin . . 137
Editorial Announcement 137
Grant to Adolf Schmidt by Berlin Academy 193
International Conference on Terrestrial Magnetism and Atmospheric
Electricity 48
Magnetic Storm, November 21-22, 1898 193
Secular Motion of Free Magnetic Needle 193
ABSTRACTS AND REVIEWS
Von Bezold, W. : Zur Theorie des Erdmagnetismus . . L. A. Bauer 191
Bigelow, F. H. : Solar and Terrestrial Magnetism . Arthur Schuster 179
Ellis, Wm. : On the Relation between the Diurnal Range of Mag-
netic Declination and Horizontal Force and the Period of Sun-
spot Frequency G. W. Littlehales 184
Hellmann, G. : Facsimile Reprints L.A.Bauer 190
GEELMUYDEN, H. : Nogle Magnetiske Observationer i Nordmarken
og i Christiania P. Wernicke 91
Gray, Andrew : A Treatise on Magnetism and Electricity
J. E. Davies 185
Liznar, J. : Ueber die Aenderung der erdmagnetischen Kraft mit der
Hohe E. J. Wilczynski 191
Moreno y Anda, M. : Estudio Sobre el Magnetismo Terrestre en
M6xico
Observations Magn€tiques faites a l'Observatoire As-
tronomique National de Tacubaya, pendant l'annee, 1895
G. W. Littlehales 89
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viii TABLE OF CONTENTS
PAGE
Moureaux, Th. : Comparaison des Appareils Magn6tiques de Voy-
age de l'Observatoire G W. Littlehales 186
Nippoldt, A. : Neue allgemeine Erscheinungen in der taglichen Vari-
ation der erdmagnetischen Elemente . . . .E.J, Wikzynski 184
Palazzo, L. : Misure di Magnetismo Terrestre fatte in Sicilia nel
1890 C. A. Schott 88
Van Rijckevorsel: Comparison of the Instruments for Absolute
Magnetic Measurements at Different Observatories
G. W. Littlehales 187
Van dbr Stok : Observations made at the Magnetical and Meteor-
ological Observatory at Batavia J. F. Hayford 92
United States : Isogonic Charts for 1900 188
PUBLICATIONS
Recent Publications 138, 192
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Volume III Number r
Terrestrial Magnetism, Mardi}j8oS\
LE NOUVEAU PAVILLON MAGNETIQUE DE L'OBSERVA-
TOIRE DU PARC SAINT-MAUR.
Par Th. Moureaux, Directeur du Service Magn^tique.
L'observatoire du Pare Saint-Maur est une d£pendance du Bu-
reau central m6t£orologique de France ; il est situ6 au voisinage de
la Marne, k i 2 kilometres E. SE. de Tobservatoire de Paris, et k 7
kilometres des limites de la capitale. Ses coordonn£es g£ogra-
phiques sont :
Longitude, o° 9' 23" E. de Paris.
Latitude, 48 48 34 N.
La propri6te\ en grande partie bois£e, a une superficie de trois
hectares ; des rues la bordent sur ses quatre c6t6s.
Le terrain de la region appartient au calcaire grossier de Paris ;
la partie occup6e par l'observatoire a 6t6 d'abord exploited, il y a 30
ans, pour Textraction de la pierre k b&tir ; le sous-sol est tres per-
meable.
L'ancien pavilion magn£tique, construit en 1882 k Toccasion des
expeditions polaires internationales, est place* vers le milieu et au
point culminant de la propri6te\ k l'altitude de 50 metres et k 20
metres au-dessus du niveau moyen de la rivtere. Le premier mag-
n£tographe du syst&me de M. Mascart a 6te" install^ dans les caves
en juillet 1882, ainsi que les appareils k lecture directe. Les ob-
servations ont commence immeMiatement k titre d'essai ; reMuites et
publi6es depuis le i er Janvier 1883, elles forment actuellement une
s£rie non interrompue de 15 ann6es.
Construit k T6troit, avec des ressources trop mesur^es, ce pavilion
suffisait sans doute au but strict pour lequelil avait 6t6 6tabli, mais
les locaux manquaient pour les experiences sp6ciales relatives k
retude des aimants, ou k certaines particularity des ph6nom&nes
du magn&isme terrestre, particuliferement aux observations simul-
tan6es temporaires, qui n£cessitent une installation propre.
Finitr6 de Tiraportance de ces observations simultan£es, nous
avions le vif d£sir de contribuer k en assurer le succfes en France.
M. Mascart, Directeur du Bureau central m6t6orologique, ayant pu
obtenir le credit n6cessaire, il fut convenu qu'un nouveau pavilion
magn^tique serait 6tabli pour recevoir les appareils d'observation
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2 TH. MO UREA UX ivol. hi, No. i.]
courante, et que Tancien, devenu disponible, serait affectd aux ex-
periences sp&iales. Ce nouveau pavilion, isold des autres b&ti-
ments, a 6t6 construit pendant V6t6 de 1896. Nous en donnons ici
une vue photographique (Fig. 1). Sa base est un rectangle de 10
metres de long sur 6 mfetres de large, avec une avancde servant de
vestibule, et contenant Tescalier de descente aux caves; son grand
c6td est orientd dans le mdridien gdographique. Des precautions
spdciales ont 6t6 prises pour qu'aucune pi&ce de fer, aucuns ma-
tdriaux susceptibles d'action sur l'aiguille aimant£e, n'entrent dans
Figure 1.— Nouveau pavilion magnltique de l'obscrvatoire du Pare Saint-Maur
les diff£rentes parties de la construction. On s'est assurd d'ailleurs,
par des mesures directes, que le champ niagndtique terrestre n'est
aucunement alt£r6 dans l'interieur du pavilion.
Le rez-de-chauss£e forme une grande salle dallde, occupant toute
la surface du rectangle : son ameublement ne contient aucune sub-
stance magndtique; largement dclairde dans les conditions ordi-
naires, elle peut ais6ment se transformer en chambre noire.
Le faible credit mis & notre disposition n'a pas permis de r6al-
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LE NOUVEAU PA VILLON MAGN£TIQUE 3
iser tons les perfectionnements obtenus dans certains observatoires;
on n'a pu songer, par exemple, k adopter des dispositions pour as-
surer, comme k Pavlovsk, la Constance de la temperature, en toutes
saisons, autour des appareils de variations; mais, et c'est Ik le point
important, nous avons rdussi k dliminer k peu prfes complement la
variation diurne de la temperature, ainsi qu'en tdmoignent les
courbes relevdes rdguli&rement k un thermoni&tre enregistreur.
Les changements dtant extr£menient lents, les corrections rdsul-
tantes peuvent §tre calcul£es trfes exactement.
NORDi
gch^lfi
Figure 2.— Plan des caves magneiiques.
Les caves peuvent communiquer directement avec la salle du
rez-de-chauss£e, au moyen de deux ouvertures A, A (Fig. 2), qu'on
peut ouvrir ou fermer k volont£ ; en B, B, sont des chemin£es d'ap-
pel d'air dissimul£es dans le mur et correspondant avec Textdrieur
au-dessus du toit. Ces dispositions permettent d'£tablir, de sup-
primer, de rdgler, en un mot, l'a£ration des caves.
Les murs dtaient parfaitement sees lorsque nous avons pris pos-
session du b&timent, en ao^t 1897. Le plan ci-joint (Fig. 2) indique
la position des instruments dans les caves: celle du sud contient les
appareils k lecture directe; Tenregistreur photographique est en
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4 777. MO UREA UX [Vol. Ill, No. i.j
service dans la cave du nord. Sous le vestibule du rez-de-chauss6e,
une salle est disponible pour Installation future d'un s6ismographe.
Les appareils de variations, pr£alablement dtudtes, ont 6t€ mis
en place en octobre et novembre 1897 ; ils sont recouverts de cloches
en verre, et soustraits aux variations de Thumidit^. On a d'ailleurs
remplae£, dans les bifilaires, le fil de cocon de soie par du fil de
maillechort de o mra ,o3 de diamfetre. Les observations ont commencd
le i er d^cembre 1897; elles ont 6t6 faites concurremment dans les
caves des deux pavilions pendant tout ce mois. Le service r£gu-
lier dans les nouvelles conditions fonctionne depuis le ier Janvier
1898.
Des que l'ancien pavilion aura subi les reparations et transfor-
mations n^cessaires, il pourra §tre utilise pour les observations si-
multan£es temporaires, k moins toutefois que toutes les d6penses,
tous les efforts faits en vue de perfectionner et d'£tendre nos moyens
d'investigation ne demeurent stdriles. On sait en effet que l'£tab-
lissement de lignes de tramways 61ectriques k trolley dans le voi-
sinage des observatoires, a gravement compromis les etudes du mag-
net isme terrestre ou des courants telluriques a Washington, Toronto,
Greenwich, Lyon, Clermont-Ferrand. . . . : l'observatoire mag-
n£tique du Pare Saint Maur est 6galement menac£ dans son avenir
par la meme cause de trouble. Le Conseil g£n6ral du d£partement
de la Seine vient, malgr£ nos vives protestations, d'autoriser une
compagnie priv6e k substituer k un moteur k air comprint la trac-
tion electrique, syst£me k trolley, sur la ligne des tramways de
Charenton k La Varenne, ligne qui passe k 1600 metres au Sud de
TObservatoire. Bien que cette decision ne soit pas encore sanc-
tionn£e, on peut craindre que les int£r£ts de la Science, d6}k m£-
connus ailleurs, ne soient sacrifi^s £galement, dans un avenir pro-
chain, k Tobservatoire magn£tique central de France.
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THE ALTITUDE OF THE AURORA ABOVE THE
EARTH'S SURFACE. 1
By Professor Cleveland Abbe.
INTRODUCTION.
During the past three centuries, numerous observers and physi-
cists, astronomers and mathematicians, have endeavored to con-
tribute to our knowledge of the altitude of the region whence the
auroral light proceeds, and still the greatest diversity of opinion
seems to prevail on this subject. Some observers— such as Captain
Parry, Sir James Clark Ross, and Sir John Ross his uncle, Dr.
Walker, and Professor J. P. Lesley — have seen the light in such
positions between themselves and neighboring objects as to demon-
strate that the aurora, like the lightning, descends to the very sur-
face of the earth, and may even be entirely confined to the lowest
stratum.
Others— such as Dr. Richardson, Sir John Franklin, Silber-
mann — have seen it so located among the clouds that its origin
must be placed at or below their level, and therefore within a few
thousand feet of the earth's surface. On the other hand, those who
have calculated the altitudes of specific beams and arches by trigo-
nometrical or equivalent methods, have generally found figures in-
dicating altitudes between twenty and a hundred miles. Perhaps
the highest altitudes that have been deduced were the following :
Dal ton, 150 miles; Loomis, 400 to 600 ; Bergman, 468; Boscovich,
825; Fournerius, 1,006; Twining, 1,100; Kramer, 1,945 kilometers,
or 1,200 miles.
Those who delight in numerical calculations accept these larger
altitudes, and content themselves with saying that the altitude of
the aurora ranges from 50 miles upward to 1,000. The experi-
mental physicists, by studying the analogies between the auroral
light and the discharge of electricity through vacuum tubes, have
shown that the auroral phenomena harmonize — in part, at least —
with those observed in vacua such as might occur at moderate alti-
tudes; thus Miller and De La Rue give altitudes of from 10 to 40
miles.
1 A small portion of this paper was read at the Philosophical Society, Washing-
ton, April 15, 1893 ; another portion at the American Philosophical Society, Philadel-
phia, January 7, 1898.
2
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6 CLEVELAND ABBE [Vol. hi, No. i.]
Finally, the most careful observers have in many cases defended
the accuracy of the observations made under circumstances that
admit of no doubt that the auroral light, in the free atmosphere,
often emanates from points within a few yards of the observer.
Lemstrom has sought to reconcile the diverse conclusions by
maintaining that, while many auroras are quite high up and belong
to the upper air, yet those in extreme northern latitudes most gen-
erally belong to the lowest strata, and follow the unevenness of the
ground, appearing as glows around the mountain-tops, or as rays di-
rected toward prominent objects.
The object of the present paper is to collect together some of
the numerous observations, calculations, and opinions bearing on
the nature and the altitude of the auroral light. We shall not es-
pecially consider the electrical origin or the source of the elec-
tricity, but simply acquiesce in the universal conviction that it
really is one form of electrical discharge, our main object being to
ascertain whether we can in any way definitely fix its locus in the
atmosphere.
Our most instructive method of procedure will consist in taking
up the consideration of a number of authorities in chronological
order, by which means we are led to appreciate the slow progress
of our knowledge, and the difficulty which many investigators have
felt, from time to time, in giving up preconceived views without
having anything better to accept in their places. There is noth-
ing more difficult than to recognize the fact that all our ideas are
wrong, and that we are wholly in the dark with regard to the na-
ture of that which our eyes behold so plainly. How many thou-
sands of years elapsed before modern science gave us any clue to
the true nature of the rainbow, and how difficult it has been to
eradicate from our text-books the crude ideas of Descartes, Huy-
ghens, and Sir Isaac Newton, which made the rainbow to be a
phenomenon of dispersion, and to substitute the correct view of
Thomas Young, who showed it to be a phenomenon of interference !
I think it likely that we must go through a similar series of
changes in our views with regard to the auroral light, until we
recognize that each observer sees his own aurora as a so-called op-
tical illusion.
There are several forms of optical illusion that are evidently
connected with the aurora. Some of these were recognized long
since, while others are still deceiving our senses and perplexing our
calculations.
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I
THE ALTITUDE OF THE AURORA 7
As we pursue our reading chronologically, among the different
authorities that I shall quote, we shall perceive how one after an-
other is led to suspect and fully recognize some one or other of
these optical or perspective illusions, while others, inattentive
thereto, plunge deeper into misleading calculations. If at the end
of our consideration of the subject we sum up all that has been
shown to be probable or demonstrated to be true, we shall almost
necessarily conclude that the determination of the altitude of the
aurora is a much more delicate problem, and perhaps also a more
indefinite problem, than we have hitherto believed.
CHRONOLOGICAL SUMMARY.
Haixey. — In the London Philosophical Transactions for 1716,
Edmund Halley gives an elaborate account of the aurora of March
6th (Old Style), which was the first aurora that he had personally
observed ; indeed, none had been recorded anywhere in Europe for
the eighty years 162 1 to 1707, so far as he then knew. Halley
advances the idea " that subtle matter, freely pervading the pores
of the earth and entering it near its southern pole, may pass out
again into the ether at the same distance from the northern pole,
its direction being still more and more oblique as the distance from
the poles is greater." In this paragraph he applies to the earth,
considered as a great magnet, the idea that he had just previously
deduced from the arrangement of iron filings around an ordinary
magnet, and he supposes that "this subtle matter may, by the con-
course of several causes, be capable of producing a small degree
of light."
This idea that the luminous beams of the aurora emanate verti-
cally from the polar regions seems to be the same as that adopted
by Dr. Kramer in his computation quoted by Boiler in Gerland's
" Beitrage" in 1896. Halley practically recognizes that the auroral
streamers are composed of rays parallel to the free magnetic needle.
He also was the first to explain that the corona was a perspective
effect produced by viewing the rays nearly endwise. But he failed
to note the fact, published by Mairan in 1747, that the location of
the center of the corona corresponded to the south end of the dip-
ping-needle. Halley also gave these rays so great a length and alti-
tude as to "think it more than probable that these vapors were car-
ried to such a height as to emerge out of the shadow of the earth
and be illuminated by the direct beams of the sun." He further-
more recognizes that " this corona was not one and the same in all
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8 CLEVELAND ABBE [Vol. hi, no. i.
places, but was different in every differing horizon. . . . Nor is it
to be doubted but that the pyramidical figure of these ascending
beams is optical. ... By the rules of perspective, their sides
ought to converge to a point. . . . Others, being intercepted
by the interposition of the convexity of the earth, would only
show their pointed tops." Halley considers the arches as being
" two bright laminae," whose edges being turned towards us were
" capable of emitting so much light that we might read by them.
I choose to call them laminae because, though they were but thin,
doubtless they spread horizontally over a large tract of the earth's
surface." Halley was also the first to observe that the summits of
these auroral arches lay to the west of the astronomical meridian,
and practically in the magnetic meridian, though he does not men-
tion the latter point.
Hjorter, Celsius, Graham. — The fact that decided temporary
disturbances in the position of the magnetic needle occur during
an aurora was first observed by Hjorter, of the observatory at Up-
sala, in March, 1741, and, according to Poggendorff, similar observa-
tions were independently made by Celsius at Upsala, and Graham
in England; but although this subject has since then been exten-
sively studied, yet nothing more precise has as yet been discovered
relative to the connection between these phenomena.
Mairan, Maier. — Mairau 1 says that the pole of the auroral
corona is in the direction of the free dipping-needle. Furthermore,
that the aurora of 1726, October 19th, was more than 70 leagues
above the earth's surface, as computed from observations made by
himself at the Chateau of Breuillepont in Normandy, and by others
at Paris. 2 In his second "edition, pages 60-63, Mairan revises his
x TraiUde VAurore Bortale, Paris Academy, Memoirs of 1731, printed Paris,
1733; Amsterdam reprint, 1735; second Paris edition, 1754.
* Apparently, this computation was based upon the following considerations:
The center of the corona as observed at Breuillepont was 7 or 8 degrees south of the
zenith (see M&moires de V Academic, 1726, page 214) ; the center of the corona as
seen at Paris was not more than 4 or 5 degrees east of the zenith ; Breuillepont is
about 17 leagues west of Paris. In the second edition of 1751, Mairan recognizes that
this computation was hazardous, and was not unchallenged by his colleagues ; but
that at least one must conclude that the luminous matter of the aurora was far above
ordinary meteors and twilight phenomena. He finds this extreme height verified by
general considerations as to the wide extent of country over which the auroras of
September 12, 1621, March 17, 1716, and October 19, 1726, were observed. Assuming
that observers at extreme points, such as Lisbon and St. Petersburg, were view-
ing the same luminous phenomenon in their respective horizons, he calculates that
it could not have been less than 57 X leagues above the earth's surface at a point mid-
way between these extremes.
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THE ALTITUDE OF THE AURORA 9
first calculation of the altitude of the aurora observed on October
19, 1726. He combines together the altitude of the luminous arc
38 or 40 degrees, observed at Thury, which is 13 leagues north of
Paris; 37 degrees observed at Paris, and 20 degrees observed at
Frescati and at Rome. Mairan's new calculation gave him 266
leagues as the altitude of the aurora. Finally, with reference to
the aurora of October 8, 1731, he combines the altitude observed at
Copenhagen— namely, 46 or 47 degrees above the southern hori-
zon — with the altitude, 25 or 26, as observed by himself at Breuille-
pont, which is within 7 minutes of being in the same latitude as
Paris, and deduces 250 leagues as the altitude. In general, he con-
cludes that most observations give 200 leagues as the height of the
aurora; but some put it at 100, and others at 300. He adds that
Professor Cramer, of Geneva, had communicated to him 160 leagues
as the altitude of the aurora of February 15, 1730, calculated from
the apparent height of the luminous band observed at Geneva and
at Montpellier simultaneously; and Mairan adds that we must be-
lieve that the luminous matter has various altitudes above the sur-
face of the earth, depending on a variety of circumstances. On
pages 65-67, and again, pages 404-436, of the second edition, Mai-
ran considers Maier's method of determining the auroral altitude,
and applies both that and the parallactic method to a number of au-
roral observations.
Maier. — Maier 1 communicated his method to the Academy of
Sciences of St. Petersburg in 1728 (1726?); but it was not pub-
lished until 1735 by that academy, although meanwhile it had been
discussed by Maupertius before the Paris Academy in 173 1. Maier's
method assumes that the auroral arch is a circle concentric with
the geographical pole, and therefore parallel with the earth's sur-
face. His computation of altitude requires that the amplitude of
the auroral arch shall be measured by the equal distance of its two
ends from the meridian, as also the apparent altitude of the center
of the arch. It seems thus to avoid the consideration of parallaxes,
and requires only one observer and one station. Mairan gives his
reasons for preferring the parallactic method, but recognizes the
ingenuity of Maier's idea, and gives numerous comparative results
of calculations by both methods, quoting usually from Maier's sec-
ond memoir, dated 1728, but published in 1735, or six years after
his own death. Maier's method was subsequently elaborated by
1 P. C. Mayer (Meyer or Maier) : de Luce Boreali> 1726-1735.
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w
if
IO CLEVELAND ABBE IVol. hi, nc. i]
Krafft in the ninth volume of the St. Petersburg memoirs, and by
Boscovich in his notes on Noceti.
The following altitudes are published by Mairan, computed by
Maier's method and KrafTt's formula :
1621, September 12th, observed by Gassendi in Provence. Resulting alti-
tudes, 16 ? leagues (25 leagues is one degree of a great circle).
1750, February 3d, observed by de Fouchy, Paris Observatory, and by
Mairan at the Louvre. Resulting altitude, 169 leagues.
The two preceding auroras are the only cases to which Maier's
method strictly applies, according to Mairan ; but the second aurora
was also observed at Geneva by Abauzit, apparent altitude 19
or 20 ; semi-amplitude, 50 , and applying Maier's method to his
observations, Mairan obtained 134 leagues. In addition to these
three, Mairan quotes the cases computed by Krafft, namely :
1730, March 16th, observed at St. Petersburg; apparent altitude 9 , semi-
amplitude 45 . The resulting altitude, 47 leagues.
1730, September 6th, observed at St. Petersburg; apparent altitude 9 12',
semi-amplitude 42 . Altitude, 58 leagues.
1730. November 2d, observed at St. Petersburg. Apparent altitude, 12 de-
grees; semi-amplitude, 37°3o'; linear altitude, 170 leagues.
After discussing the general advantages and disadvantages of
the parallax method, Mairan next gives the results of computations
of altitudes by this method; namely:
1726, October 19th, observed at Paris and Rome, and also at Thury and
Copenhagen. The latter observation, by Horrebow, located the arch through
the zenith, and gave" an altitude of 187 leagues, while the observation of the
arch through the zenith at St. Petersburg gave 266 leagues; and Mairan at-
tributes this difference in a general way to the difficulty of observing so near
the zenith, to the great distance between the meridians, and to the imperfect
observation through the clouds at St. Petersburg.
1732, September 1st, arch observed at Paris and at Copenhagen. Result-
ing altitude, 214 leagues.
1732, November 12th. Concerning this aurora, Mairan remarks that it
was not visible to him at Breuillepont, 18 leagues west of Paris. This fact
ought to have awakened one who was not committed to any preconceived
theory to a realization of the fact that the aurora is probably a very local phe-
nomenon, and that no good could come from the combination of observations
of arches at Paris and Copenhagen when no arch, and even no aurora, was
visible at Breuillepont. However, he makes the calculation, and obtains 74
leagues.
1734, February 22d. Not visible at Breuillepont until later in the even-
ing. The observations at Paris and Copenhagen gave 211 leagues.
1735, February 22d. An unusually well-defined arch, observed by Mairan
at Paris and Horrebow at Copenhagen. Resulting altitude. 165 leagues.
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I
THE ALTITUDE OF THE AURORA n
1736, December 22d. This is the only one of two cases in which the ob-
servations made by Celsius, at Tornea in Bothnia (65 5i / N., or 420 leagues
north of Paris), could be combined with observations at Paris. This aurora,
on the nth of December (Old Style, or the 22d of December, New Style),
passed through the zenith at Tornea at 7.45 P. M., and at the same time ap-
peared at an altitude of 14 or 15 degrees above the north horizon at Paris.
The resulting altitude is 194 leagues.
1737, January 21st, observed at Paris and Tornea. Result, 155 leagues.
1737, December 16th. This was a famous aurora, observed over a large
part of Enrope. Boscovich, from observations at Padua and England, had
deduced 348 leagues, but afterwards reduced this to 275 leagues. Mairan, from
observations at Paris and Moutpellier, gave an altitude of " about 200 leagues."
1 740, November 3d. This is the only one out of thirty observed at Up-
sala by Celsius for which Mairan could find another corresponding observa-
tion for the application of his parallactic method. From observations at
Upsala, and those made by himself at the Chateau de Sain-port or Saint As-
sise, he deduces 157 leagues. Mairan faithfully records the fact, that according
to Celsius, a series of luminous arches successively rose from the north-north-
west throughout the whole evening, and passed the zenith of Upsala, or ex.
panded about the zenith in different curves. He therefore assumes that the
arch seen by himself, at an altitude of about 22 degrees above the horizon of
the Chateau de Sain-port, was one of those that passed the zenith of Upsala.
1750, February 3d. This is the same that was computed above by Maier's
method. Mairan applies his parallax method to observations made by D'Ar-
quier at Toulouse (apparent altitude, 14 or 15 degrees), Abauzit at Geneva
(altitude, 19 or 20 degrees), and de Fouchy at the Paris Observatory (apparent
altitude, 26 or 27 degrees). The result is "about 173 leagues" for the com-
bination Toulouse-Paris; 154 leagues for Paris-Geneva; 175 for Toulouse-
Geneva.
To the above list, Mairan adds the following:
1730, February 15th. A luminous band observed at Geneva and Mont-
pellier ; result, 160 leagues.
1726, October 19th. Arch observed at Paris and Rome ; result, 266.
173 1, October 8th. Arch observed at Copenhagen and Breuillepont ; re-
sult, 250 leagues.
These 22 computations on 16 different auroras are tabulated on pages
433-434, whence the mean altitude is 175 leagues, the extremes being 47
and 275.
Young. — Dr. Thomas Young, in his course of lectures on nat-
ural philosophy, Vol. I, 1807, P a ge 7 l6 » says: "It is doubtful
whether the light of the aurora borealis may not be of an elec-
trical nature; the phenomenon is certainly connected with the gen-
eral cause of magnetism ; the primitive beams of light are supposed
to be at an elevation of at least 50 or ioo miles above the earth, and
everywhere iu a direction parallel to that of the dipping-needle;
but, perhaps, although the substance is magnetical, the illumina-
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1 2 CLE VELAND ABBE [Vol. hi, no. i.)
tion, which renders it visible, may still be derived from the pas-
sage of electricity at too great a distance to be discovered by any
other test." In his second volume, pages 488-490, he gives a bib-
liography of the literature of the subject, and quotes Mairan's opin-
ion that the aurora is about 200 leagues above the earth, and his
determination of the fact that the dipping-needle points to the pole
of the aurora. He also refers to the fact that Hoxton (Phil. Trans.,
1731) found the magnetic needle agitated during the aurora, that
Winn (Phil. Trans., 1774) observed that the aurora was generally
followed the day after by a storm from the south or southwest, and
that Blagden and Gmelin (Phil. Trans., 1 781) gave several testimonies
as to a rustling noise heard during the aurora. He furthermore quotes
Cavendish's computations (Phil. Trans., 1790), showing that the
height was between 52 and 71 miles, and mentions that Cavendish
added that the diffused nature of the light may make the appear-
ance different in different places, and thus make distant observa-
tions fallacious.
To be continued.
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ON THE INVESTIGATION OF HIDDEN PERIODICITIES
WITH APPLICATION TO A SUPPOSED 26 DAY PERIOD
OF METEOROLOGICAL PHENOMENA.
By Arthur Schuster, F. R. S.
1. Obvious and Hidden Periodicities. A variable quantity
may show periodic changes which become obvious as soon as a
sufficient record has been obtained; such are the semi-diurnal changes
of the tides, or the eleven years recurrence of sunspot maxima. We
may call these obvious periodicities. Most often, however, small
periodic variations are hidden behind irregularlmctuations, and their
investigation then becomes a matter of considerable difficulty. The
lunar influence on the daily variation of magnetic forces may serve
as an example of such hidden periodicities. In the case of lunar
effects the investigation of the periodicity is facilitated by our pre-
vious knowledge of the period ; but additional difficulties arise when
the periodic time is one of the unknown quantities. We possess a
number of investigations dealing with a periodicity of various ter-
restrial phenomena, supposed to be coincident with that of the time
of revolution of the sun round its axis. But although several
authorities have considered the existence of such a period as proved,
the scientific world has only reluctantly and very doubtfully ac-
cepted its reality. Nor can it be said that this scepticism is not
justified, for no one has so far discussed the very essential question
whether the results obtained may not be due to merely accidental
circumstances.
It is the object of this paper to introduce a little more scientific
precision into the treatment of problems which involve hidden perio-
dicities, and to apply the theory of probability in such a way that
we may be able to assign a definite number for the probability that
the effects found by means of the usual methods are real, and not
due to accident.
2. Summary of thb Usual Method of Finding a Hid-
den Periodicity. If it be required to investigate a possible pe-
riod of p intervals in a series of numbers t x , t 2 , / 3 , etc., it is usual to
solve the problem by some process analogous to the one which is
briefly indicated in this paragraph. Let the numbers be arranged
3
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V
'4
ARTHUR SCHCSTER
[Vol. HI, No. i.|
according to the following scheme, where // stands for tp + , , //' for
t 2 p - 1 , etc.
'3'
1— I *— I
*
(I)
t x t 2 t, 7>
^1 , ^2 . etc., represent the sums of the vertical columns. The quan-
tities T may be expressed by a periodic series of the form :
S = a + a x cos -f a 2 cos 2^-f . . . a p cos / *
+ b x siu + £ 2 sin 2 -j- . . . bp— x sin (/ — 1) ,
where S= T x if we substitute = — , and generally 5* becomes T q
by the substitution of = .
/>
The coefficients are determined by a well known process, which
gives
fi a =T l +T 2 +T,+ T p
kpa l = TiCOS#+ 7 , 2 cos2^+7 , 3 cos3^+ . 7^ cos/ 91 ^ 2jr
lpb t =T x sinO+T 2 s\n2»+T s sin^^ . . T A smp#) ~~ p
a is therefore equal to the mean value of all the quantities T or to
s times the mean values of all the quantities /. If there is a well
marked periodicity corresponding to p intervals, we should expect
the value of r, -- V a x 2 + b x 2 to have a markedly greater value than
when no such periodicity exists, and we may take the quantity
P = — -, as a measure of the amplitude of the periodicity correspond-
do
ing to p intervals. The quantity p is determined by the equation :
(2)
4 " 4** 2
(7 , ,cos0 + 7;cos2" +
T P Y
(7;sin0 +7;si n2^+ . . T p smp») 2 ( .
T x +f 2 + . . . T p )* (3;
(7;+ t 2 + .
3. Probability for Different Values of the Ampli-
tudes if the Original Numbers are Chosen at Random.
The first question which arises refers to the relative probability of
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INVESTIGATION OF HIDDEN PERIODICITIES 1 5
different values of p, calculated on the supposition that no true
periodicity exists.
We may confine ourselves to such cases as may occur in nature,
and fix our attention, say, on events like thunderstorms, earthquakes,
or magnetic storms. Supposing it is required to investigate a pos-
sible period of p days, we should form the Table (1), entering for /
the number of events which have happened on a particular day.
Thus, if we are discussing a 30 day period of earthquakes, p would
be equal to 30, and if 2 earthquakes occur on the the 33d day we
should write t 3 ' = 2. The Table (1) being formed, and the values
of p calculated, our problem may be stated thus : What is the prod-
ability that p should lie between any two assigned values p x and p 2 , on
the supposition that the events are distributed quite at random ? Before
proceeding to calculate this, I put the question in a rather more
general form. The number p of intervals, into which the whole
period is divided, may be chosen as large as we please ; and each
interval may be made as small as we like. It may be an hour, or
a minute, or a second. If this process is carried sufficiently far,
equations (2) become,
pa = n
i P &i — cos k tj + cos k t 2 -f- . . . . + cos k t„ (4)
£ p b x = sin k t x + sin k t 2 + . . . . + sin k t n ,
where n is the total number of events and k stands for -y, T being
the whole length of the period, and t x , t 2 , etc., the times of occurrence
of successive events. (The quantities T x , T 2 do not occur in the
future investigation, and their confusion with T is therefore not
possible.) Equation (3) becomes
^ii = J (cos k t x + cos k t 2 + . . . cos k t H ) 2 +
2a t.
(sin k t x + sin k t 2 + . . . sinkl n y\ i * (5
The meaning of the right-hand side of this equation is best illus-
trated by means of a diagram. On a circle with center at 0> choose
a number of points P x , P 2 , such that the angle between the lines
O P l and O P 2 and a fixed direction are kl 1} kt 2l etc. li OP ly O P 2
represent forces of equal intensity but different directions, the right-
hand side of (5) gives the magnitude of the resultant. If the events
may happen with equal probability at any time, the points P x , P 2
-will be distributed over the circle in such a manner that any di-
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1 6 ARTHUR SCHUSTER ivol. hi, no. i.)
rection of the line OP lf 0P 2i is equally probable. It has been
shown by Lord Rayleigh, 1 in a paper " On the Resultant of a large
number of vibrations of the same pitch and arbitrary phase," that
the probability of the resultant having a value lying between s and
s + d s in that case is
— e"sds, (6)
n
n being the total number of vectors which are combined.
It is a simple matter to pass from this result to the solution of
our problem. From (5) and (6) it follows that the probability of
the value of — - lying between — p and — O 4- dp) is
2a„ 6 2 2 v J
pe
« dp (7)
2 '
and this is therefore also the probability that the quantity — , which
do
we have taken as the measure of the amplitude of the periodicity f
lies between the values p and p + dp. The expectancy for — is
do
^(^ e -^r dp = SI=Ul. (8)
2 J o V * V n
Similarly the expectancy for I — J
is
2J0 n
(9)
The probability that the value of — exceeds p is
<*0
» -?^
pe
A d? = e 4 • ( IO >
Our result may now be expressed as follows :
If a number n of disconnected events occur within an interval of
time T, all times being equally probable for every event \ and if the
1 Phil. Mag. Vol. X, p. 73 (1880) II.
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INVESTIGATION OF HIDDEN PERIODICITIES
17
frequency of occurrence of these events is expressed in a series of the
form
I 1 t—r l t—r 2 . t—T p \
a^i + /> I cos27r-^ 7 -- + /> 2 cos4tt-y 1- .... J rPpCOS 2pK-Y~^\ y
the probability that any coefficient p has a value lying between p and
P + d p is
— pe dp
2
and the expectancy for p is A |— .
\ n
In proving the proposition, it was assumed that the number p
of intervals into which the period T is subdivided, is very large;
but this condition is not essential. To suit accurately the process
employed in actual calculations we should have to consider the
vectors OP lt O P 2 , to be confined to fixed directions forming angles
2 ic
— with each other. But it follows directly from the method em-
P
ployed by Lord Rayleigh in his proof that his results must apply
to this case also if p is a multiple of 4. Further, the expression for
the expectancy of p 1 can be shown to be the same for all values
of/. It is not necessary to inquire whether equation (7) also holds
in the most general case, when p y for instance, is an odd number,
because the process of calculation illustrated by the tabular arrange-
ment (1) and the result (2) is justified only when p is so large that
a further increase in p would not produce any material change in
the value of the coefficients of Fourier's series. We may therefore
accept equations (7), (8), (9) and (10) as applicable to all cases which,
concern us.
Equation (8) gives the expectancy of />, t. e. y its mean value when
a great number of cases are treated. It is seen to vary inversely as
the square root of the total number of events. Thus if 10,000 events
are subjected to the Fourier analysis, the expectancy for the coeffi-
cient p is 0.0177, and the probability that p is greater than the
IT
expectancy e 4 is 0.456. The probability that p is greater than
irk*
k times the expectancy is found from (10) to be e 4
4
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i8
ARTHUR SCHUSTER
[Vol. Ill, No. i.]
To facilitate the application of our result to individual cases, I
have calculated in Table I the function e 4 for different values
of*,
Table I.
ir A* 1
1
n A*.
k
e 4 !
t k
1
e 4
O.I
i
0.9922
«
0.2145
0.2
0.9691
1 1.6
0.1339
o-3
0.9318
1.8
0.07850
0.4
0.8819
2.0
0.04321
0.5
0.8217
2.5
0.00738
0.6
0.7537
3-o
0.0008514
0.7
0.6806
35
6.63 iX 10-5
0.8
0.6049
4.0
3.487X10-*
0.9
0.5293
4-5
1.238X10-7
1.0
0.4559
50
2.967X 10—9
1.2
0.3227
The use of the table is as follows: Find the coefficients of
Fourier's series; a nt b n being two corresponding coefficients and
a the constant term, calculate p = ; next calculate the
<*>0
1.77
expectancy (e) for p, from the formula e = 77= where n is the
p
total number of observations, and form the ratio k = — . The
€
above table will then give the probability that the quantity p is
still greater than the one found.
Thus, if for 10,000 observations the quantity p is found to be
0.035, ^ would be 2, and we should find that in one case of 23 a
still higher value would be obtained for /», if the events take place
at random. Such a value for p would not justify us therefore to
consider a real periodicity as proved, although we might be encour-
aged to continue the investigation by taking an increased number
of events into account. If, on the other hand, the quantity p is
equal to 3 or 4 times the expectancy, the table shows that there
is a reasonable ground for supposing the events not to be dis-
tributed at random.
Our equations will also allow us to fix beforehand the number
of events we must take into account in order to discover a periodic
effect of a given magnitude. This is best illustrated by an example.
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» INVESTIGATION OF HIDDEN PERIODICITIES 19
Let us wish, for instance, to discover whether there is a lunar period
in magnetic storms. What is the number of magnetic storms we
must take into account in the calculations, if the periodic term is of
such magnitude that the number of magnetic storms occurring
within a certain time near the maximum should bear the ratio
1 + * to the number of storms occurring on the average during
the same time throughout the lunation ? To be reasonably certain
of the effect, the fraction ^ should be equal to at least three
times the expectancy calculated on the supposition of an arbitrary
distribution ; putting therefore A = 3 -J — we find for the number
of storms required
q * 28.3
Thus if ^ is to be one per cent, n must be at least 28,000. This shows
how futile it is to attempt to discover small periodic effects unless
a great quantity of material is at our disposal.
4. Occurrence of Events in Groups. The expectancy of
amplitude may be increased considerably if the events do not take
place at random, but are apt to bccur in groups. Thus, for instance,
if any one wanting to study a small periodic variation in the num-
ber of sunspots, were to count each spot as a separate " event," the
average amplitudes of the periodic series would be found considerably
in excess of our calculated expectancy on account of the tendency
of sunspots to form groups. The following reflection will show
this to be the case. It is clear that if, in our previous deductions,
we consider each event to be entered in the tabular arrangement
(2) as m instead of as 1, the quantity we have called p would not be
altered, while the total number of events would be m times as much
as before, and the expectancy obtained from (8) would be reduced
in the ratio V m : 1, which is not the correct value. We may, how-
ever, generalize our equations, so as to be applicable to this case.
If the events occur in groups of m t the probability that the quantity
P lies between p and p-\-d p becomes equal to
n 4« ,
e pap
2 m
and the expectancy becomes
'•77 yj T
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20 ARTHUR SCHUSTER [Vol. hi, no. i.]
More generally still, if there are n t groups of m t events, n 2 groups
of m 2 events, etc., the total number being N, all quantities n lt n 2i etc.,
being large, the probability that the coefficient lies between p and
P + dp is
jvV
2(«,w, 2 + «^ 2 H . . . . ) e p p
and the expectancy is
V it (», jk x 2 + »2 rn 2 2 + . . . ) /„)
5. Periodicities in the Daily Values of Fluctuating
Quantities. We have so far considered periodicities which may
appear in the occurrence of detached events, each event being con-
sidered as of equal magnitude. But there is another class of perio-
dicity which requires a somewhat different treatment. I mean a
periodicity in magnitude of a quantity which recurs at equal inter-
vals, the former case being a periodicity of occurrence of quantities
of equal magnitude. Thus we may wish to investigate lunar perio-
dicities in the daily average of barometric pressure, or of the daily
mean of magnetic declination. The calculation of Fourier's coeffi-
cients is carried out exactly as in the former case. In the tabular
form (1), the quantities t lf t 29 denote now the daily values which it
is intended to analyze, and equations (2) hold as before. Writ-
ing again r l = V a t 2 + b? , we deduce from (2)
I/r I ={(r i cos0 I +7;cos20+ . . . ) 2 + (^sin^+7;sin2<9+ . . .)*}*.
The quantity on the right-hand side is the sum of vectors T ly T 2 ,
etc., acting in directions which form angles 0, , 2 & t , etc., with some
fixed direction, and remembering that T t , T 2 , etc., is each made up of
a sum of quantities t ly t 2t etc., the problem to be solved is equivalent
to the following :
A number of vectors of varying magnitudes act in p fixed di-
2 T
rections, forming angles equal to — with each other; The number
of vectors in each direction being equal to s t what is the probability
that the resultant exceeds any given value R f It will be sufficient
to consider the case that the probability of positive and negative
2 T
vectors is the same in all directions. If, further, — - is a submultiple
of a right angle, the result may be written down at once from Lord
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I
INVESTIGATION OF HIDDEN PERIODICITIES 2 1
Rayleigh's investigation. If there be n x vectors of magnitude a h n 2
vectors of magnitude <h , etc., the probability that the resultant vector
has a magnitude intermediate between R and R + dR is
_ &
•e "i* , + -* ,+ ' RdR .
n x a x * + « 2 a^ +
It follows that the probability that r z has a value intermediate be-
tween p and p + dp is
/V
2 (»,«,* + *«,'+ . . . ) ' ^*
The expectancy of r z is — V n («i a? + * 2 a 3 * + . - . )
and the expectancy of r x 2 is -^ («i 01* + » 2 a a 2 + . . . ) .
If the vectors are distributed according to the law of errors, so that
the number which have a value intermediate between p and ? + d P
2hN ~ h% P
is — j=e dP , N being the total number of vectors and h a
V n
constant, it follows that
2 AN r°° -* f *V JV
Hence the probability that the coefficients in Fourier's series have
a value intermediate between p and p~\-dp becomes
The expectancy of the coefficients becomes
/n 2
and the expectancy of the square of the coefficients
2^
It has been assumed that Fourier's analysis has been applied to the
quantities T in (1), but if, as is more rational, we treat directly the
quantities /, we must write N for p in the preceding results.
The results of this paragraph are summed up as follows : Let a
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22 ARTHUR SCHUSTER [vol. hi, no. i.j
number of quantities t lt t 2 . . . t H be treated by Fourier's analysis,
the quantities all being independent of each other and distributed
according to the law of errors, so that the probability that any quan-
tity / has a value intermediate between fi and ? + dft is
2 te dp.
V n
The probability that any coefficient of the periodic series has a
value intermediate between p and p + dp will then be
Nh*e % ^pdp.
The probability that the coefficient exceeds p is
and the expectancy for the coefficient and its square is respectively
1 [JZ
h\2N
and
N Nh 2 '
If the law which regulates the distribution of magnitude of the
quantities t is not the law of error, the preceding results will also
give the proper values for the expectancy, provided we substitute
Nh 2 =- 2 (*, «, a + n 2 a 2 * + . . . ) .
6. Limitation of the Preceding Results. The results
of the preceding paragraph are deduced on the supposition that
the values of the fluctuating quantity on successive days are quite
independent of each other. This is seldom the case. If we were
to take quantities, like the average height of the barometer during
24 hours on successive days, and were to investigate possible
periodicities of these daily averages, our previous results could not
be applied, for the barometric pressure on any one day is not inde-
pendent of the pressure on the previous day, a high barometer being
more likely to be followed by a high than by a low barometer. The
effect of such regularities must be taken into account, and their
effect will generally be to diminish the amplitudes of the shorter
periods. When there is no connection between the individual quan-
tities, all coefficients of Fourier's series are equally probable, but
any regularity will favor certain periods as against others If we
draw a curve at random on a sheet of paper, we cannot assign any
definite value to the probability that a coefficent of the Fourier
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INVESTIGATION OF HIDDEN PERIODICITIES
23
series should exceed a given value, unless we take account of the
particular bias of a person, which determines the average slope
he gives to the lines. If, on the other hand, we were to rule a num-
ber of closely adjacent vertical lines, and place a point at random
on each, the continuity being destroyed, the results obtained in the
preceding paragraphs will hold, because the successive points of
the curve are now independent. Some regularities nearly always
exist, even if they do not appear at first sight ; and it is of the great-
est importance to be clear as to their effect whenever periodicities
are to be looked for. Let us take as an example the case of sunspots,
and admit, for the sake of argument, that there is no regularity at
all in their distribution ; that, for instance, a certain number of sun-
spots appear on the average every year, but that their appearance
on a particular day is purely regulated by the laws of chance, and
that the life of all sunspots is the same. The latter fact introduces
a regularity. If the number of sunspots appearing on successive
days were analyzed by Fourier's series, the period which is equal
to the life of a sunspot would disappear, and shorter periods would
all be reduced in magnitude, but not to an equal amount, so that
the result might show periodicities which are caused by the
fact that all spots have the same length of life. If, as is the case in
reality, the lives of sunspots are not the same, yet follow some law
of distribution round an average value, investigations on sunspot
periodicities are affected in as far as the periods approximately
equal to the average life are reduced in amplitude, and that by
contrast, therefore, periods which are decidedly longer will seem
to be increased.
7. Optical Analogy. Regularities like those discussed in the
preceding paragraph will have the effect that the expectancy of
the values of the Fourier coefficients depends to some extent on
the period; but there will not in general be any well-defined
maxima for particular periods, unless there is some definite periodic
cause. The problem, which, so far, has only been treated by the laws
of probability, must now be approached from a different point of
view. Let /(/) be any variable function of the time, and consider
the integrals
A=C 1 f(f)coskt dt , B=C l f(t)sinkt dt . ( I2 )
The quantity R = 1/ a* + £* will depend on the values of k, t u
and T; but supposing t t is altered while k and T remain the same,
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24 ARTHUR SCHUSTER [vol. hi, no. i .] j
the values of R calculated for a great many values of t x chosen at *
random, will in all cases which we are now considering fluctuate
about some mean value R \ At any rate, we may exclude from our
discussion any case in which this is not true. This value of R!
may depend on k> and the problem with which we are concerned
consists in determining in what way it does depend on k t and par-
ticularly whether there are any well-defined maxima for certain
periods. It will be seen that Fourier's analysis here serves the
same purpose as the prismatic analysis of a luminous disturbance.
The irregular fluctuations of light give continuous spectra, and
complete irregularity means equal amplitude for all periods.
" Lines" or "bands" are produced by greater or smaller regularity
in the luminous disturbance. This optical analogy is a very impor-
tant one, and we may translate some well-known optical theorems
into useful propositions concerning the general analysis of fluctuat-
ing quantities. If, for instance, in optics we are dealing with a
"double line" — i. e., a superposition of two nearly equal periodicities
— we know that the separation of the lines depends on "resolving
power." The resolving power is proportional to the quantity T in
the above equations, and just as a spectoscope of low resolving
power is insufficient to separate two lines which are close together, so
shall we be unable to distinguish between two periodicities of differ-
ent frequencies, unless the time limits are sufficiently extended. In
optics we seldom use a resolving power lower than that required
to separate the two sodium lines. To accomplish such a separation
the quantity T'must include 1,000 periods; that is to say, in the case
of a 26 day period we should have to take into account a series of
observations extending over not less than 70 years.
It is easily seen that the number of lines on a grating deter-
mines the optical resolving power exactly in the same way as the
lumber of periods taken into the account in investigations like the
ibove.
8. The Periodogram. It is convenient to have a word for
>ome representation of a variable quantity which shall correspond
:o the "spectrum" of a luminous radiation. I propose the word
beriodogram, and define it more particularly in the following way
Let
h Ta=$f(J)Qoskt dt , i Tb = §f(£)smkt dt . (13)
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\ INVESTIGATION OF HIDDEN PERIODICITIES 25
where T may for convenience be chosen to be equal to some integer
multiple of -r-, and plot a curve with -y as abscissae and r = Vd 2 + b 2
as ordinates ; this curve, or, better, the space between this curve and
the axis of abscissae, represents the periodogram of /(/). A few
examples may be given in illustration. The periodogram of the
sound emitted by an organ-pipe or a violin string consists of a series
of equidistant "lines." A noise would be represented by a periodo-
gram showing a broad band. The periodogram of sunspots would
show a "band" in the neighborhood of a period of eleven years,
while the periodogram of tides would have a line coincident with
the lunar month. The periodogram of temperature has long lines
for the year and the day, and shorter lines for their submultiples.
The periodogram as defined by the equation (13) will in general
show an irregular outline, and also depend on the value of / x . In
the optical analysis of light we are helped by the fact that the eye
only receives the impression of the average of a great number of
adjacent periods, and also the average, as regards time, of the intensity
of radiation of any particular period. If the value of r in the periodo-
gram shows maxima, this may be due to accidental circumstances,
and we must find the easiest methods of separating the accidental
from the real periodicities.
9. Separation op Accidental prom Real Periodicities.
If we were to follow the optical analogy we should have to vary
the time t x in equations (12) continuously and take the average
value of r obtained in this way for each value of k. By repeating the
process for different values of k we should ultimately be able to
decide whether there is any real periodicity ; but this would involve
an almost prohibitive labor. The following considerations simplify the
investigation. Give to /, the successive values, o, T t 2 T t etc., up to n T }
and call the corresponding values of a, b t r\ a lt b l} r lt « 2 , b 2 , r 2y etc.
The quantities r may now be taken to be vectors having compo-
nents a and b t any angle defined by tan 9 = — will be equally
probable for all vectors, if there is no real periodicity and it
the value of T is chosen sufficiently large. This last condition is
rendered necessary by the regularities alluded to in § 6. If, for in-
stance, we were to investigate barometric heights, and T were to be
taken equal to one day, while -r when chosen equal to one month,
successive values of— 1 , — , would have a tendency to be nearly equal
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26 ARTHUR SCHUSTER [Vol. in, no. i.]
and not altogether independent of each other, on account of the
persistent states of high or low barometers. But we have no reason
to suspect any connection between the barometric heights after a
time interval of, say. one year, and if T is therefore put equal to one
year, the independence of successive values of would be secured.
This being the case, we can apply results already obtained, for the
magnitude of r will in all cases depend on some law of probability.
If therefore n represents a very large number, and we form the vector
R= V A 2 -+- B 2 irom the equations
— TA=(f(t)co$ktdt, — TB=( /(t)$inkt dt , (14)
we may consider R to be the resultant of all the vectors r x , r 2t . . . r m
and if amongst the latter there are »„ of magnitude * x , n 2 of mag-
nitude a 2 . . . . the expectancy tor R and R 7 , according to § 5, is
4
and
4 ( n i a t 2 + n * a 2 2 + • . ) n x ax 2 + n 2 a 2 * + . .
But the quantities n u n 2t etc., will vary proportionally to n. As the
law according to which A and B varies, with increasing values of n t
must be the same as that of the variations of R, we have the follow-
ing two important propositions :
1) If /(f) is a function of/ which fluctuates about some mean
value in an irregular fashion, the integrals
/
T T
/(/) cos k t d t and /(/) sin k t dt
will with increasing values of T fluctuate about some average value
which increases as V T.
2) Taking R = V A 2 + B 2 when A and B are defined by (14),
and writing R f for the mean value of R f if different values of t x are
_TtX 2
taken, the probability that any particular value exceeds A R is e —
4
This last result follows from the investigation in § 5.
The condition under which these results hold is that the values
of/(/) and /(/+ T) are entirely independent, where, however, T
may be as large as we please. If there is a true period -r- contained
in/(/), this condition does not hold. By writing /(/) —coskt, it is
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INVESTIGATION OF HIDDEN PERIODICITIES 27
easily seen that the above integrals will fluctuate about some
average value which increases as T instead of as V T f and we have,
therefore, here a criterion to decide between accidental and real
periodicities. To decide between the two, it would be necessary to
form the integrals
T iT \T
f f(t)coskt dt % C/(t)coskt dt f C f(t) cos£/ dt . (15)
and by successive additions calculate the values of
/(/) cos k t dt , J /(/) cos k t dt , etc. up to I /(/) cos k t dt.
If these integrals increase on the whole proportionally to 1 w, it
would show that the successive values of (15) are wholly independ-
ent of each other; but if there is a more rapid increase, it would tend
in
to show that f(t) contains some true periodicity -r%
There is another method of securing the same object. It has
been shown that if we form the periodogram as defined in the § 8
by calculating
.'i + Jr 2 *)i
-f(<.f>w
2 r 'i + T 2 ").
coskt dt) + (J /(/)sin)fc/ dt) V
for different adjacent values of k t the quantities r will fluctuate about
some mean value r' so that the probability of r being greater than
A r' is e 4 , the condition being that there is an equal probability
for all values of k within the range considered. The chances that
r is greater than four times its mean value are exceedingly small, as
shown by table (1); and if the periodogram shows a sudden elevation
at any point corresponding to a particullar value of k which is
greater than 4 times its average value, we may conclude with
reasonable certainty that /(/) contains a periodic term, having a
period — . The second method, although not so direct as the first,
will be more easy to apply when we are looking for variations, the
periodic times of which are not accurately known. We must in any
case include different values of k into our calculations, and we need
not extend the time limits as much as would be necessary if we
were to apply the first method. It must be noted that the values
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28 ARTHUR SCHUSTER [vol. m,
of k should not be taken to lie too close to each other, as otherwise
the values of r would not be independent, for the integrals
T T
( J(J)coskt dt and f f(t)cosK t dt
will not differ much from each other if k T differs from V T by less
than about 45 . To secure complete independence, it will be better
to let (tf — k) t be as much as 90 .
1 o. Exam ples. We possess a number of investigations on hidden
periodicities which allow us to apply the second test explained in
the last paragraph. Professor Balfour Stewart 1 has published some
calculations made in conjunction with Mr. William Dodgson on
periodical variations supposed to be common to solar and terres-
trial phenomena. Their method consisted in finding, by means of
a neat and well chosen system of calculation, a numerical value for
the inequality of 27 closely adjacent periods between 23.5 and 24.5
days. Table II gives their result for the temperature ranges at
three stations during 16 years. By temperature range is meant
the difference between the daily indications of the maximum and
minimum thermometers. The numbers are not exactly the co-
efficients of the corresponding term in the Fourier expansion, but
are approximately proportional to them, and for our present pur-
pose may be taken to represent the ordinates of the periodogram.
A glance at the table will show that the distribution of the figures
is very much what would be expected on the theory of chance.
The mean ordinates found from the table are, 3639, 3740, and 31 17,
and the maximum ordinates are equal to 1.6, 1.5, and 1.7 times the
mean ordinates respectively, while the minima are equal to 0.38,
0.48, and 0.46 times the mean ordinate. Reference to Table I will
show that there is nothing in these figures to indicate any true
periodicity, as, on the theory of chance, one case out of every 13
should give an amplitude more than 1.8 times the mean amplitude,
and one in every 8 one smaller than 0.4 times the mean one. The
other tables given in the same paper show similar variations, and if
we look at the results obtained by the authors, keeping in mind the
variability of the inequalities which may be expected by the rules
of chance, we come to the conclusion that there is no evidence
either in the temperature range or in the declination range of any
periods in the neighborhood of 24 days.
1 Proceedings Royal Society XXIX (1879), p. 303.
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INVESTIGATION OF HIDDEN PERIODICITIES 29
Table II.
Exact period
Magnitude of inequality
in days
Kew
Utrecht
Toronto
23*5400
2IOO
1922
2934
23 5729
3093
3080
1422
23 '<x>57
4700
3950
2252
23 '6386
4025
398o
4446
23*715
1386
1887
3030
3939
23 *7043
2624
5246
23 7372
39"0
2166
3638
23 77O0
3915
1780
2622
23 -8029
3UO
3992
2148
23*8357
2771
4540
3337
23-8686
4234
4578
3422
23 9014
5921
4624
2906
23 '9343
5518
3878
3098
23 9671
2374
2572
2772
24*0000
3912
2586
3428
24 0329
5135
3958
2863
24*0657
4516
2984
1678
24-0986
2157
3394
3902
24*i3i4
2378
5392
3216
24-1643
3795
5690
336o
24 -1971
3926
3350
4274
24 2300
3043
2520
2728
24 '2628
2520
4342
5802
2377
24 2957
3004
3258
24 *32»5
4302
5572
3601
24 *36i4
476i
5146
2400
24*3943
5824
3832
2906
Mean: 3639 3740 3 117
As a second example I take Unterweger's 1 attempt to prove va-
riations in sunspot activity having periods of 28, 30-5% and 36 days.
The process employed is similar to that of Balfour Stewart. Twenty
different periods, called trial periods, varying between 24 and 37
days are taken, and their amplitudes are found to be as follows :
8.4, 12.5, 7.3, 9.8, 12.6, 13.3, 17.1, 6.9, 12.2, 6.0, 17.4, 19.1, 13.9, 15.5,
8.0, 1 1.6, 15.9, 12.6, 20.8, 12.8.
It is argued that the highest amplitudes, 17.1, 19. 1, and 20.8,
stand out sufficiently above the rest to give evidence in favor of a
true periodicity; but as the mean of the above number is 12.7, and
as by the probabilities an amplitude equal to more than twice
the mean ought to occur in about one case out of every 23, it is
seen that the figures are just such as we should expect by the laws
of chance.
11. Length ok Record Necbssary to Establish Perio-
dicities. It follows from Table II that, if fluctuations are of a
1 Denkschrifl d. math.-naturw. Classe d. kais. Akad. d. Wissensehaften (Wien),
Vol. LVIII.
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3 o ARTHUR SCHUSTER ivol. hi, no. u
purely accidental character, the ordinate of the periodogram would
only once in 300,000 cases rise to four times its mean value. The
abscissae, as has been pointed out, must be taken sufficiently far
apart for the ordinates to be independent of each other. If we
adopt the limits given at the end of § 9, it would follow that two
periods T' and T y for which the amplitudes are calculated, should
be sufficiently far apart to satisfy the equation
1 11
V^V>^T
where T is the whole time. If, for instance, the observations taken
during one year are treated, and the periods surrounding 26 days are
considered, it is found that the difference between two periods should
amount to at least 0.54 days, if the amplitudes found are intended
to be independent of each other. There may, of course, be other
reasons for taking the periods nearer together. If a periodicity
having an amplitude b is to be separated from amongst other irregu-
lar variations, it would follow that b must be at least equal to four
times the mean amplitude to afford reasonable security against de-
ception by accidental circumstances. As the mean height of the
periodogram has been shown to vary inversely as the square root
of the time space considered, we have the following rule for separat-
ing accidental and real periodicities :
If the record of a number (n) of days has been subjected to anal-
ysis by Fourier's theorem, and the mean amplitude of the periodo-
gram is found to be a t the number of days (N) required to establish
with reasonable certainly a true periodicity of amplitude b is
. r 16 a 2 n
If a probability of one in a thousand is considered a sufficient guard
against accidental periodicities, the number N may be reduced by
half.
12. Spurious Periodicities. It can not be too often insisted
upon that whenever Fourier's theorem is applied to finite intervals
of time, the resulting periodic series gives correct values only within
that interval. In consequence, the analytical calculation may give
periodicities not inherent in the function /(/) at all, but due to the
discontinuities at the limits. Those familiar with the theory of
optical instruments will be aware of the fact, that when a homo-
geneous vibration is examined by means of a spectroscope, the prin-
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INVESTIGATION OF HIDDEN PERIODICITIES 3 1
cipal line has a number of companions on either side. These com-
panions are assigned to diffraction effects ; but any one unacquainted
with the theory of undulations might be misled to believe that the
luminous body emitted light which is not altogether homogeneous.
We may call such periodicities "spurious." They are due to the
above-mentioned discontinuity at the limits, and may occur in all
problems in which Fourier's analysis is applied. In order to illus-
trate the bearing of this on the examination of hidden periodicities,
I will take a strictly periodic function cos q /, and show that when,
analyzed by Fourier's theorem within a finite range, it will, in addi-
2 9T
tion to the true period — , show certain other "spurious" periods.
2 T
In order to examine the amplitude of a possible period —r- in cos q /,
we calculate the value of r = V a 2 + 6 2 where
1 r 7
— Ta= I cos qt cos ktdt
T
— T6= f cos q t sin kt dt .
2 t
If the time ^includes n periods equal to —r it follows that
— Ta = —— 1 - T - sin a cos a (16)
2 q 2 — k 2
— 7 6 = ^-— 2 sm 2 a (, 7 )
q — k
when a is wntten for * n 2 — =- — .
k
Hence r = — r— r — - lq 2 cos 2 a -f- k 2 sin 2 a) * .
q + k a
The value of r is small except when q and k are nearly equal, and
in that case we may with sufficient accuracy write
sin a
As r has several maxima besides the principal one for which a = o,
i. e. q = k, we have here something exactly analogous to the dif-
fraction images in spectroscopes. The maxima of amplitude take
place when tan a = a. At the first maximum, which is the only
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32 ARTHUR SCHUSTER ivol. hi, no. i.j
one which need be considered, a — 1.43 r. If r is the time of the
true periodicity, r' that of the most important spurious period, it is
found by substitution for the value of a in terms of r and r' that
'-(-* 1 ?)
Thus, for instance, if we were to discuss a year's record of tidal
observations in order to see what periodicities there are, the known
period of 29 53 days would give spurious periods, the principal ones
of which are obtained by putting in the above equations n = 12, be-
cause a year contains nearly 12 complete periods. We should thus
find these spurious periods to have lengths of 26.10 and 32.96 days.
As periods of about 26 days are habitually put down to solar ro-
tation, we might be misled to believe in an influence of solar rotation
on tides. The spurious periods are easily recognized by the fact
that they depend on the time space included in the calculations, and
they approach the true period more and more as that time space is
extended. If in equations (16) and (17) k and q are nearly equal,
we obtain as a first approximation — = — tan a. Hence, if in that case
the value of cos q t is expressed in terms of Fourier's series between
the limits / = and / = —7— , the first periodic term is repre-
sented by
^cos(£/ + a) (18)
where a = * # *—? — .
k
13. The " Smoothing Process." A few words should be said
on the common practice of "smoothing down" an irregular series
of numbers before submitting them to periodic analysis. This is
done by forming a new series, taking successive and overlapping
means of, say, 4 or 5 numbers. The process is only justified if the
second series is so regular that the periodicities which were hidden
in the original series now become obvious. But whenever this is
not the case, so that Fourier's analysis has to be applied, the
labor spent in the process is wasted, and its effect often very
deceptive. In order to determine the result of smoothing on the
coefficients of Fourier's series, let us begin by taking a periodic
function cos k t. The process of taking overlapping means is equiva-
lent to substituting for coskt an expression formed from it by
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INVESTIGATION OF HIDDEN PERIODICITIES 33
taking at each time / the average value of the function in the
interval / — t to / + T , when t is a constant. This average value
isgivenby: { v + r ,
— I cos£/ dt = -r- sin kr cos kt .
2T J t __ r kr
The result is again a periodic function, but with an amplitude di-
. . , • . A - .. sin£r
minished, in the ratio — 7 — .
kr
In the general case, where the function y.—f(t) need not be
periodic, we may substitute by Fourier's theorem,
f(fl = -Lf dk C /(X)cosk(t — X)dk
where the limits and T have been chosen, so as to make the
problem correspond to the actual process used. We now form a
new variable
/= ) f[t)dt .
Performing the integration, we find
y ' = T§TV ldk f/(*)<x>sk(l-X)<U . (20)
o o
This equation is approximate only owing to the fact that when /
is smaller than r or greater than T — r , the integration involves
values of / for which the equation (19) does not hold; but if T is
large compared to r, the error introduced is negligible. The result
shows that the periodogram is reduced everywhere in the ratio
?i^ , the period being ^ . The process of smoothing, therefore,
has completely destroyed periods equal to kr or submultiples
thereof. This, no doubt, was the object of those who employed it;
but they do not seem to have noticed that the other coefficients are
also affected in a manner which might easily lead to a belief in
imaginary periodicities. To show this by au example, take the case
that a 26 day period is looked for and the material treated as ex-
plained in § 1, after taking overlapping means of 5 successive num-
bers. If there is no true period, the expectancy for the coefficients
of Fourier's series is the same, and therefore no regularity is to be
expected in the numbers which we have called 7\ But the process
of smoothing reduces the expectancy of the first coefficients in the
6
it'
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34
ARTHUR SCHUSTER [vol. hi, no. i.)
ratio of 0.94, and the others successively in the ratios 0.77, 0.54,
0.27, 0.04. The consequence is that, a fictitious appearance of
regularity might be introduced into the numbers T y prominence
being given to the periods of 26 days as compared with that of its
submultiples. There is little doubt that the regularities artificially
introduced by the smoothing process have been the cause of fre-
quent mistakes.
14. Elimination of Secular Variations. Very consider-
able labor has sometimes been spent in eliminating secular varia-
tions and other known periodicities before the hidden periodicities
are searched for. We may reasonably ask the question, what object
is thereby gained ? It is one of the great advantages of Fourier's anal-
ysis that each of its terms is independent of the others ; and if we wish
to determine any particular coefficient, it is unnecessary to begin
by eliminating the others. The analysis itself performs that process
in the best possible way, if the coefficients are obtained by arith-
metical calculations. In some cases, however, when mechanical
processes are employed, it may be better to get rid of known varia-
tions before the unknown ones are searched for ; and this is particu-
larly the case if the former are large compared to the latter. The
best method of procedure must be settled in an individual case ; but
the general rule may be given, that it is the best to eliminate as few
variations as possible, and to carry out the elimination at as late a
stage of the computation as possible. Known variations may be
got rid of at the end by expressing them separately in a periodic
series. Thus a uniform change, such as is often assumed in the case
of secular variations of terrestrial magnetism, may be expressed by
— -= where ? is the change taking place in the time T. Expressed
in a periodic series between the limits of time / = o and / = T we
have
— E=—1- + JL / S in*/ + — sin 2*/ + — sin 3*/+ . . .1
t 2 ' *r I 2 3 ^ J
2 7T
where for shortness k is written for — .
If, therefore, the uncorrected figures for, say, the magnetic decli-
nation give a series
a + a x cos k t + a 2 cos 2 k t +
+ b l sin k t + b 2 sin 2 k t +
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INVESTIGATION OF HIDDEN PERIODICITIES 35
we correct for the effect of secular variation by leaving the a coeffi-
cients as they stand, and subtracting — from the b coefficients. This
n tz
method of treating the problem has not only the advantage of
greater simplicity, but it gives us also a clearer idea as to magni-
tudes and uncertainties of the corrections we apply.
15. Meaning of the Term "Period." Some confusion has
arisen owing to a certain vagueness in the use of the term "period."
If a quantity varies according to the symbolical expression cos k t ,
it is generally agreed to call -7- the "period" of the variation.
Strictly speaking of course, the quantity is periodic, not only in a time
-= ff but also in a time ~ , j, etc. ; yet no one would call the multi-
2 7T
pies of -T- the " period "of cos k t . In investigations of more com-
plicated periodicities the term is, on the contrary, often applied in
a loose way, and we meet with statements affirming, for instance,
a periodicity of 26 days, "the variable having two maxima and two
minima within the range of that period." This ought to be called
a 13 day period as distinguished from a 26 day period. The matter
is, I think, o' greater importance than might at first sight appear.
In a complicated subject a clear nomenclature helps towards clear
ideas. I think, therefore, it would be well to apply the term diurnal
"period" solely to a periodic change which goes through one cycle
in 24 hours, and to distinguish it, therefore, from the semi-diurnal or
ter-diurnal periods. If we wish to have a name for the complete
change including all periods which are submultiples of the princi-
pal one, it would be better to use a more general term such as di-
urnal "oscillation" or diurnal "variation."
16. Distinction between Cause and Effect. The con-
fusion alluded to in the last paragraph has, like others in this subject,
arisen from an insufficient distinction between the analytical rep-
resentation of a certain variable in terms of a periodic series and
the causes, which may perhaps quite indirectly have produced the
periodicities. The apparent cause of the tides, for instance, is the
revolution of the moon in one lunar day ; but the forces which cause
the tides have a period of half a lunar day, and this is the period of
the tides. No one confuses the time of revolution of the disk of a
siren with the note given out by it, and similarly we should draw
a clear distinction between the time of revolution of the sun or
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36 ARTHUR SCHUSTER [vol. hi, no i]
moon and the periodic times of any variables which possible may be
due to solar or lunar rotation.
I am at present only concerned with the best methods of dis-
covering periodicities, and not in finding their causes ; but it may be
worth while to lay stress on the fact that periodicities are some-
times produced by a combination of circumstances, and that when
we have discovered a periodic effect, it is not necessary to ascribe it
to something which " revolves" in the time of the period which has
been found. Thus periods approximately equal to those ascribed
to solar rotation may be produced by a combination of an annual
and a monthly period. Let an effect depend, for instance, on the
moon's declination (<*), in such a way that it is proportional to cos <J,
but is also dependent on the sun's position with respect to the
equator, and may be analytically expressed by
(a + b cos D) cos <*
when a and b are constant, and D is the sun's declination. A simple
trigonometrical transformation changes the expression to
a cos<* + i b [cos (a + Z>) + cos (* — D)\ ,
and the last two terms represent periods of 2 * I —r ± I . If / and
T denote the length of the lunar day and solar year respectively,
the length of the periods into which the whole effect resolves itself
contains terms having periodic times given by H =— -±-^r .
Substituting /=27.3, 7*-= 365.2; becomes equal to 25.4 and
29.5 days respectively. If the lunar effect is a fortnightly one, the
smaller value for would be 13.16, or half of 26.32. A period of
this kind might easily be mistaken for one due to solar rotation.
17. The 26 Day Period. This period has already been alluded
to. As it would be a matter of some importance to establish its
reality, we may illustrate some of the results obtained by a short ref-
erence to the principal researches on the subject, amongst which
Hornstein's papers deservedly take the first place. In an investi-
gation published in 1871 l Hornstein analyzes the records of the
magnetic elements. He groups, for instance, the daily values of the
declination at Prague in 1870 in the manner explained in § 1. Tak-
ing 15 trial periods, the results are collected in a table which is here
reproduced (Table III). The first column gives the number of days
1 Wiener Ber. LXIV, p. 62 (1871).
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INVESTIGATION OF HIDDEN PERIODICITIES
37
in the period chosen, and the second column gives the representation
of the value of declination, neglecting all terms in Fourier's series
except the first.
Table III
Period Declination ^
16 days 12° i'.ii -f C/.03
17
18
19
20
21
22
23
24
25
255
26
26.5
27
28
sin (x + .
sin (x -f .
sin (x -f .
sin (x -j- .
sin (x -f- .
sin (x 4-
sin (x 4-
•)
•)
1 .09 -f o .12
1 .11 4- o .07
1 .07 -j- o .19
I .IO 4 O .12
I .I3 + O.I9
1.12+0.13
1 .09 4- o .10 sin (x -f
1 .16 4- ° .10 sin (x 4-
1 .20 -j- 0.172 sin (x 4-
1 .16 -j- 0.336 sin (x +
1 .17 4- o .616 sin (x + 123 4')
1 .23 -f o .696 sin (x 4- 174 18')
1 .21 4- 0.660 sin (x 4- 2 1 7 4o / )
1 .24 4- o / .28i sin (x 4- 326 18O
.)
)
)
3°22 / )
70 o')
If the amplitudes in the table are examined, it is found that
it is on the average o'.i2, while the period 26.5 days gives a value
which is more than 5 times as great. According to Table I,
there is here a very strong evidence that this periodicity is not
due to mere accident, and a further confirmation may be found
in the gradual change of phase as the trial periods gradually in-
crease from 25 to 28 days. For, according to (18), the expression
for the first term of Fourier's series for a trial period -7- is
sin «
cos (k t 4- a)
2n , Q — k
> — — *» ±
if the true period is - and a = n n ^—7 — where n is the total number
q k .
of periods included in the time interval. In the present case n = 14.
Putting £ = 26.5
2tt
= 25, we find a = 151*
jx sln a e.
and = 0.16,
while the difference in phase in Hornstein's table which should be
equal to a is 17 1° and the ratio of amplitude 0.24. Considering the
superposition of accidental variations, these numbers are in good
agreement. But a closer examination somewhat weakens the argu-
ment. In order to see how far lunar effects might have something
to do with the periodicity found, I have extended Hornstein's calcu-
lations to the periods of 29, 30, and 3 1 days. I find for the ampli-
tudes of the first terms of Fourier's series 0.105, 0.189, and 0.157,
which is decidedly higher than the numbers given by Hornstein's
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I
M
38 ARTHUR SCHUSTER [vol. hi, no. i.]
for the periods below 24 days. I was then struck by the fact that
the amplitudes given by Hornstein were not, when casually examined,
borne out by his material.
I recalculated, therefore, some of the coefficients, and found for
the amplitude of the periods of 26, 26.5, and 27 days the values
o'-54, o'.6i, and o'.58, which are decidedly smaller than those given
by Hornstein, while for the period of 21 days I obtain a value
.295, which is decidedly larger than that of Hornstein. Hornstein
states that he has obtained the amplitudes of all periods up to 24
days inclusive by a " graphical process,*' and it would seem, therefore,
that the process must have given too small values. The corrected
numbers raise the ordinates of the mean periodogram, and weaken
considerably the evidence in favor of a true periodicity.
It should be said that an absolute check of Hornstein's calcu-
lations is not possible, because he does not state how he has elimi-
nated the secular variation, and there is some indirect evidence
that he has unknowingly strengthened the 26.5 days period by
his treatment of it. This only confirms what has been pointed
out in § 14, that it would be better to eliminate such variations after
Fourier's analysis has been applied. We may pass more quickly
over the remainder of Hornstein's paper. The declination at Vienna
during the same year shows a variation for a period of 26 days,
which is little more than double that found for a period of 24 days,
and no certain conclusions can be based on so slight a preponder-
ance. The results for the inclination are equally undecisive, while
those for the horizontal intensity give a mean ampitude of 7.7 units
of the fourth decimal place, while the greatest among 15 amplitudes
is 17.0. Here the results are, therefore, entirely such as we may
expect to be due to accidental variations.
In a subsequent paper Hornstein endeavors to prove the exist-
ence of a 26 day period in the daily variation of barometric press-
ure, but I must express my opinion that he has failed to establish
his point. His method of procedure consists in forming the series
of numbers T (see (1) § 1), the amplitude of the diurnal period
having been grouped in periods of 24, 25, 26, 27, and 28 days. In-
stead, however, of applying Fourier's analysis to the numbers 7, he
sums up the figures irrespective of sign, and thus obtains what he
considers to be a measure for the amplitude of the period. The
figures found are: 222, 298, 490, 245, 226, for the five periods
respectively, the largest number belonging to the 26 day period.
Even if we could accept Hornstein's method of deducing the
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1
1
1"
INVESTIGATION OF HIDDEN PERIODICITIES
39
amplitude, the figures would not prove much; for the largest of
them is less than twice as great as the average. But a closer in-
spection shows that the 26 day series gives a large value, because
it contains the highest and lowest numbers, viz., -f- 85 and — 58; but
these appear on two successive days. If, therefore, Fourier's analysis
were applied, we should get a large value for the amplitude, not of
the 26 day period but of the two day period, and it is practically
certain that the close juxtaposition of such a high and low value
can only be due to accident. Hornstein specially remarks that
Fourier's series, when applied to his numbers, would be misleading;
but there is no reason for this statement beyond the fact that
Fourier's series would not support the 26 day period. I have cal-
culated the first coefficients of the series, and find them to be equal
to 146, 176, 109, 155, 132, for the five periods respectively, so that
the 26 day period now gives the smallest instead of the largest
value.
Hornstein's work was soon followed up by Lizuar, Miiller, and
others, who adopted very much the same method of procedure,
taking trial periods of 24, 25, 26, 27, and 28 days, and calculating the
amplitude of the first term of Fourier's series. Table IV gives a
summary of the principal results obtained.
niodi
1 I
11
in
IV
V
VI
VII
VIII
IX
24
O.0812
0.0463
0.4404
2682
1724
0.0401
0.0476
24.48
5.85
25
O.I 00 1
0.2042
0.9627
2873
6173
0.2 IOI
O.1 196
36.23
36.39
26
0.2262
0.3258
0.549I
3295
3239
0.2327
0.14 16
44.22
41.27
27
0.1920
0.1678
0.9822
4278
2393
0.1295
0.1006
31.54
28.35
28
0.0528
0.1620
0.3100
2080
1288
0.1007
0.0445
15.52
10.64
The numbers given refer to the amplitudes where the periods
are those stated in the first column. The variables in the different
vertical columns are as follows :
I. The amplitude of daily variation of declination at Vienna
(1882 — 1884), calculated by taking the difference of the observation
at 2 p. m. and 8 a. m. on each day. 1
II. The same for Kremsmunster.
III. IV, V. The daily variations according to Liznar of decli-
nation, horizontal intensity and vertical intensity at St. Petersburg.
VI, VII. The easterly and westerly disturbances at Vienna. 2
VIII, IX. The disturbances of horizontal and vertical intensity
at St. Petersburg.*
» Liznar. Wiener Ber. Vol. 94, p. 834 (1887).
* Liznar. Wiener Ber. Vol. 91, p. 474 (1885).
8 Mueller. Bulletin of the Akademie of St. Petersburg. 1886.
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4 o ARTHUR SCHUSTER [vol. hi, no.
An inspection of the numbers leads to the following con-
clusions :
i. Each column by itself is not sufficient to prove the existence
of a 26 day period, the ratio of the greatest to the smallest ampli-
tudes being in no case greater than one might expect from the
theory of chance.
2. There is, however, the significiant fact that in six out of the
nine columns the greatest amplitude falls on the 26 day period, and
in no case does it fall either on the 24 or the 28 day period. It is
difficult to believe that this is due to accident.
As regards the length of the most probable period which seems
indicated in the above tables, Adolph Schmidt 1 calculates it to be
25.87 days.
One of the most striking arguments in favor of a periodicity
connected with the above is that derived from von Bezold's calcula-
tions on the occurrence of thunderstorms. The tables given do not
allow us to apply the results of the previous pages; but the fact
that, according to von Bezold, no trial period has given him ampli-
tude similar in magnitude to that of 25.84 days, together with the
similarity in the numbers obtained separately from two different and
independent time intervals, renders it unlikely that the results are
due to mere chance. But it should be understood that it is really
the first submultiple of the 25.84 day period; /. e„ a period of 12.92
days, which gives the exceptionally large amplitude.
Prof. Frank H. Bigelow 2 has discussed a supposed connection
between solar rotation and meteorological phenomena, in a series
of papers.
The period he adopts is 26.68 days, which differs materially from
that arrived at by Liznar, Miiller, and von Bezold, but more nearly
agrees with that deduced by Hornstein for the magnetic declination.
Unfortunately, Professor Bigelow does not, as tar as I know, give
anywhere sufficient details to allow us to apply our methods of
testing their reality. The curves he gives in support of his
views would, however, imply that it is the fourth or fifth sub-
multiple of his period, rather than the period itself, which gives
the largest effect. The general result of a critical examination
of the published investigations on the 26 day period leads me to
think that, although the magnetic elements and the occurrence of
thunderstorms seem to be affected by a period of 26 days and of its
1 Wiener Ber. XCVI, p. 989 (1887).
* Meteorological Journal, September, 1893; and other publications.
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INVESTIGATION OF HIDDEN PERIODICITIES
41
first submultiple, the subject requires a good deal of further study
before we can be sure as to the exact nature of the period. Even
though it may be considered as proved, it must not be necessarily
assumed that it is due to solar action.
If it was a question merely of magnetic disturbances, there does
not seem to be any great improbability, however, that some perio-
dicity may be connected with the sun's rotation about its axis, espe-
cially at times of great sunspot activity. Groups of spots have
been observed to persist for several rotations. If a large group is
likely to be accompanied by a magnetic disturbance, that disturbance
may easily be repeated after a complete revolution of the sun. The
result of such an action would not be a " homogeneous " period, or a
" line " in the periodogram as we have called it, but rather a broad
band having its center at a period coincident with the average
period of revolution of a sunspot. It would seem therefore that
the most promising line of investigation would be to determine the
shape of the mean periodogram taking account of a sufficiently long
time interval. I am at present engaged in treating the Greenwich
observations of magnetic declination from this point of view.
18. Conclusion. The importance of calculating the mean
periodogram has been pointed out in the last section, and, quite
independently of any research as to particular periodicity, I be-
lieve that great interest attaches to it in many meteorological phe-
nomena. The periodogram, for instance, of the changes of barometric
pressure would seem to me likely to give important information.
It has been shown that if the height of the barometer on one day
were perfectly independent of that on the previous day, all periods
would be equally probable, and the mean periodogram would be a
straight line. In virtue of the persistence in the duration of high
and low barometers, the mean periodogram will show maxima and
minima, and nothing is known as to their position. It must be of
interest to find out whether different localities show any marked
differences in the periodogram, and it is almost certain that places
which lie near a track along which frequent cyclones are passing
will show characteristic differences in the periodogram. Similarly
periodograms of temperature are likely to prove of importance.
7
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THE RELATION OF TERRESTRIAL MAGNETISM TO GEOLOGY.'
It has long been known that just as the secular variation of the mag-
net is accompanied by minor diurnal changes, so the large alterations in
the direction of the compass and dipping-needle, which are observed
when we move from place to place on the surface of the earth, are af-
fected by irregularities which are due to purely local causes. Thus the
declination is greater in Ireland than in England ; but the increase is not
uniform as we pass from one country to the other. In fact, in some
districts an abnormally large increase is followed by a decrease.
These curious inequalities must be due to local disturbing forces, and
the large number of observations which have been made in this country
[Great Britain] have enabled us to determine with more than usual ac-
curacy the magnitude and direction which the magnetic forces would as-
sume if they were undisturbed by any local cause, and from the differ-
ence between things as they then would be and things as they actually
are, we can calculate the magnitude and direction of the disturbing
forces themselves. When these are represented on a map, it is found that
there are large districts of the country in which the disturbing horizon-
tal forces act in the same direction ; in one region the north pole of the
needle will be deflected to the east, in another to the west, and, as we pass
from one of these districts to the other, we always find that at the
boundary the downward vertical force on the north pole of the needle
reaches a maximum value. We are thus able to draw upon the map
lines toward which the north pole of the needle is attracted. It is found
that the exact position of these can be determined with considerable ac-
curacy, and that the lines can be traced without any possible doubt
through distances amounting, in some instances, to a couple of hun-
dred miles. The key to this curious fact is probably furnished
by observations in the neighborhood of great masses of basalt or
other magnetic rocks. If these were magnetized by the induction
of the earth's magnetic field, the upper portions of them would, in
this hemisphere, attract the north pole of the needle; and it is found
that where large masses of basalt exist, as in Antrim, in the Scotch
coal-fields, in North Wales, and elsewhere, the north pole of the needle
is, as a matter of fact, attracted towards them from distances which may
amount to fifty miles. The thickness of the sheets of basalt is in most
cases too small to furnish a complete explanation of the observed facts,
but it is quite possible that these surface layers of magnetic matter are
merely indications of underground protuberances of similar rocks from
which the surface sheets have been extruded. At all events, there is no
possible doubt of the fact that where large masses of basalt occur, the
north pole of the needle tends to move toward them.
There are other regions were the attractions are manifest, but where,
» Extracted from " Recent Researches on Terrestrial Magnetism," by Prof. A. W.
Riicker, F. R. S. Nature, Dec. 23, 1897, p. 183.
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TERRESTRIAL MAGNETISM AND GEOLOGY 43
nevertheless, no magnetic rocks occur upon the surface ; but it is most
probable that the cause is the same, and that it is due to the mere accident
of denudation that in one case we can, and in the other we can not, point
to the magnetic rocks to which the anomalous behavior of the compass
is due. If this be so, it is certainly interesting that magnetic observa-
tions should enable us to penetrate to depths which the geologist can
not otherwise reach, and that the lines which we draw upon the surface
of the map, as those to which the north pole is attracted, may, in fact,
roughly represent the ridge-lines of concealed masses of magnetic rocks,
which are the foundations upon which the deposits studied by the geol-
ogist have been laid.
There is some ground for thinking that if these great underground
wrinkles exist, they have affected the rocks which are superposed upon
them, especially those which are of a comparatively early date. As a
general rule, if older rocks appear in the midst of newer ones, the pole
01 the magnet will be attracted towards the protruding mass ; but this
rule holds good only of the rocks of carboniferous or pre-carboniferous
age, and does not apply to later deposits. As a striking example, I may
state that the Pennine Range — which is sometimes called the "Back-
bone of England " — is a mass of millstone grit rising amid younger
rocks. Down this a well-marked magnetic ridge-line runs. Similarly,
in the neighborhood of Birmingham, the Dudley and Nuneaton coal-fields
are surrounded by more modern deposits. A curious horse-shoe shaped
ridge-line connects these two, and then runs south to Reading, which is
magnetically speaking, one of the most important towns in the kingdom.
Hast and west from Dover to Milford Haven, and then across the English
Channel to Wexford, runs a ridge of the older rocks, called by geol-
ogists the Palaeozoic Ridge, concealed in many places by newer depos-
its. Hollowed out in this are the South Wales and Forest of Dean coal-
fields, and in another hollow within it lies the coal which has recently
been discovered at Dover. Closely following this protruding mass of the
older rocks is a magnetic ridge-line which passes through Reading, and
thus we have a magnetic connection between the anticlinals of War-
wickshire and the Palaeozic Ridge. From the neighborhood of Reading
also another magnetic ridge-line runs southwards, entering the channel
near Chichester. M. Moureaux, who, with most untiring energy, has for
many years been investigating, single-handed, the magnetic constitution
of France, has discovered the continuation of this line on the French
coast near Dieppe, and has traced it through the north of France to
some fifty miles south of Paris. The energy which is now being dis-
played by magnetic surveyors in many countries will, no doubt before
long, prove that the network of these magnetic ridge-lines is universal,
and the relations between them and the geological conformation of the
countries in which they lie will be so studied that our inductions will
be based upon an adequate knowledge of facts.
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NOTE IN REGARD TO MAGNETIC DISTURBANCES ON ST.
GEORGE ISLAND, BERING SEA.
The Pribilof Islands, in Bering Sea, are entirely volcanic in origin.
St. George, the second in size of this group, is somewhat over twelve
miles in length and five miles in width. Its surface is strewn with lava
rock and scoria, except around the borders of the island, where there is
a heavy growth of grass. There are, however, no well-marked volcanic
craters as on the sister island of St. Paul. During the progress of the
plane table surveys made by the Coast and Geodetic Survey parties on
the latter island, it was noticed that there were considerable local varia-
tions in the magnetic declination. Opportunity was afforded to investi-
gate this subject somewhat on St. George Island, while waiting for the
arrival of the revenue cutter that was to take the party off. Besides reg-
ular magnetic observations at a base station, the declination was deter-
mined at twenty-four other points distributed over the eastern two-thirds
of the island. These observations were made with a regular magnet-
ometer, the true directions of the lines being obtained from the triangu-
lation of the island. The declinations observed showed a range from 5
14' East of North on the highest central hill, Ulakiya, to 20 o3 / East on
the northeastern shore of the island. Another station on the summit
of Ulakiya showed declination of 5 54', while at three stations within
a quarter of a mile, and north, northeast, and southeast of the summit,
the declinations were 14 55', 15 38' and 15 27', and at no other place
on the island was the declination observed less than 14 00' East. The
variations appear to be due principally to the magnetic properties of the
local surface materials. Small pieces of the volcanic rock and scoria
held near the magnetometer were found to deflect the needle by as much
as a quarter of a degree. Around a red scoria bank near the village of
St. George, the declination varied nearly three degrees in about sixty
feet.
As the disturbances appeared to be due to local surface conditions,
no attempt was made to investigate the irregularities in the other mag-
netic elements, the dip and force. The observations on St. George are
of interest as indicating the amount of deviation of the magnetic needle
that may be expected on volcanic islands Cases of much greater local
deflections than these have, however, been noted in other parts of the
earth. As far as observed, the direction of the needle varied about 6°
around the shores of the island, and it is probable that at the distances
at which ships would approach the island the effect would be consider-
ably less than this, so that these magnetic irregularities might not ma-
terially affect the compass in navigation. G. R. Putnam,
U. S. Coast and Geodetic Survey.
44
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LETTER TO EDITOR
NEUE BEITRAGE ZUR SAMMLUNG ALTERER ABWEICHUNGS-
BEOBACHTUNGEN. 1
Seit der Mittheilung (Kon. Akad. d. Wiss. Sitz. 27. Febr. '97) iiber die
Resultate der Bearbeitung gesamraelter Materialien, sind diese nicht
unwesentlich vermehrt worden. Chronologisch geordnet, tnit Hinzufu-
gung einiger vorlaufigen Angaben, sind diese Beitrage die folgenden :
1 . Le Discours de la Navigation de Jean et Raoul Parmentier de Dieppe;
publiepar Ch. She/er. Paris, 1883.
U. a. liest man im Journal : "18 Juin .... 1' orient fut pris a 47 30',
la hauteur a midi 36 19'; V Occident & 79 30^; de longit. orientale 15°."
Die Reduction dieser und noch 5 anderer Amplitude-Beobachtungen
W. v. Gr.
lieferten :
1529, Juui 8.
I7°20 /
N. O.
27°20 /
S.
Br.
6<
11.
22 20
i<
31 O
<(
3
12.
23 O
<(
32 30
<<
1
16.
17 O
it
35
n
5
18.
15 O
<<
36 20
*'
9
20.
14 O
'*
37 40
"
12
Ein Vergleich mit den Beobachtungen Joao de Castro's im Jahre 1538/
die mit spateren sehr gut ubereinstimmen, ergiebt eine Sacular- Variation
von verdachtiger Grosse. Nur die erste in obiger Tabelle macht eine
Ausnahme. Shefer meint, dass hochstwahrscheinlich Crignon der Ver-
fasser des Journals ist.
2. Abbildung eines Kompasses auf einer Karte von Palestina : Jac.
Ziegler, Syriae ad Ptolemaici operis rationem .... 1532. Nordenskiold
hat die Karte in seinen Facsimile- Atlas (pg. 105 der englischen Ausgabe)
aufgenommen und auf diese Abbildung aufmerksam gemacht.
Hellmann (Die Anfange d. Magn. Beob. Zeitschr. f. Erdk. XXXII)
weist auf die abnorme Grosse der Abweichung (etwa 25 W.) hin, und
sieht in ihr nicht mehr als eine Angabe, dass die Abweichung an der
Kiiste Palestinas westlich ware. Da die Abweichung An fangs des i6ten
Jahrhunderts in jenen Gegenden nur sehrklein war, und bei den Bousso-
len Nadel und Lilie zusammenfielen, scheint mir indessen dieser Schluss
zu gewagt.
3. Die Beobachtungen von Stephen und Christopher Borough. (Onkel
und Neffe.) Diese (s. "Hackluyt" I) sind fast immer ubersehen worden.
Sie sind:
Stephen Borough :
1556 Juli 17. 3°30 / N. W. 69°ic/ N. Br. 55 c/ O. v Gr. Miindung der Pet-
chora.
" Kussow Insel.
" Kiiste Waigatz.
" Colmogro.
" Bei Dogsnose.
" Bei 3 Inseln an der
Kiiste Kola's.
I Der Amsterdamer Acad em ie der Wissenschaften durch Herrn Kammerer Onnes
am 27. Nov. 1897 mitgetheilt.
27-
7 30
" 7o 42
' 57 30
Aug. 6.
8
" 7o 25
1 59
1557
5 10
M 6 4 25
4 4i 50
Juni 2.
4
" 6 5 47
1 40
16.
3 30
" 6659
1 39 30
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4 6 »'• I'AX BEMMELEX vou in. No i.]
Christopher BoRorGH:
1580 April 17. i3°4</ N. W. 46°2i' N. Br. 4S 5 * O. ▼. Gr. Astrachan.
Juiu 1 1.- 16. 10 40 " 40 25 49 30 •' Rildih.
Oct 4. 11 o " 42 5 " 4$ 15 M Derbent
4. D.el r Arcane del Mare, de Roberto DudUo. Firenze, 1646.
Die zahlreichen auf den Karten eingezeichneten Abweichungswerthe
sind bereits von Ch. Schott fur die Sammlung Xord-Amerikanischer
Beobachtungen benutzt worden. Ich glaube, es ist unrathsam, sie far
die Epoche 1600 anzufuhren; erstlich, weil es ersichtlich ist, dass Dudley
viele nach Muthmassung und nicht nach wirklichen Beobachtungen
eingezeichnet hat; zweitens, weil hochst interessante Beobachtungen,
welche Dudley zweifellos bekannt waren, nicht eingezeichnet sind ; drit-
tens, weil die Angaben nicht fur einen bestimmten Punkt gelten, sondern
sich iiber ein Gebiet von mehreren Graden erstrecken. Es finden sich
aber in jenem Werke einige Portulane vor, welche hochst interessante
Beobachtungen en thai ten.
Das Erste enthalt die Beobachtungen, welche Abram Kendal auf
Dudley's Fahrt im Jahre 1594 angestellt hat In West-Indien zeigt sich
wenig Uebereinstimmung mit meiner Isogonenkarte fur 1600; ein
naheres Urtheil behalte ich mir vor.
Ein anderes hat die Ueberschrift : "Portulano quinto del Mare del
Zur con la California, d* un Piloto Inglese valente, fin' air Isole Filipine."
Aus dem Verlaufe der Reise ergiebt sich mit Gewissheit, dass man es
hier mit derjenigen Cavendish's zu thun hat Folgende Abweichungen
werden angefuhrt:
1587 April 2°30 / N. \V. 34° o' S. Br. 7i°39 / W. v. Gr. Maipo.
Mai 25. 2 o N. O. 2 45 80 o " Puna
Aux. 20" 13 15 N. 104 o ** >!auranilla?
2 o ** 20 45 " 106 o ** Kap Corrientcs.
30 4 * 22 55 *' 1 1 1 56 t§ Kap S. Lucar.
Die mitgetheilten Langen ennoglichen es, die zwei Beobachtungen,
welche Kircher citirt und Carlheim-Gyllenskiold benutzt hat, zu beur-
theilen. Wie ich schon friiher glaubte schliessen zu diirfen, ergeben
sie sich als werthlos.
Das dritte Portulan riihrt von einem gewissen Davis her (vermuth-
lich Davis of Limehouse, erste Reise der Englander nach OsMndien)
in welchem jedoch die Langen zu unsicher sind, als dass man ihnen
Werth beilegen konnte.
Auf der Karte der Hudson's Bai finden sich einige Abweichungen,
mit Verweisung auf Hudson's Fahrt 1610-11, wiihrend es doch sehr
unwahrscheinlich ist, dass Dudley die verloren gegangenen Beobachtun-
gen dieser Reise gekannt haben soil.
5. P. Sarmiento de Gamboa fand in Port Bermejo 1579 keine Abweich-
ung (S. Theil III der Hackluyt Society, pg. 93 und J. Burney, A Chron-
Hist. etc. II, pg. 4)-
6. Unter den MSS. Delists (D6pot de la Marine, Paris) ist eine Karte
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LETTER TO EDITOR
47
Bellini's : "Carte Marine universelle ou Ton voit l'e*tat de la Variation
en 1600 suivant les observations de Gilbert en 1600, celles de Stevin en
1599, celles de Dudley en 1594, celles de Dalenis de Figueiredo en 1609,
celles de Champlain en 1604, celles de Castelfrancs en 1603 et celles de
Barentson en 1594, de Spilberg en 1602, de Candish 1588 et de Davis
1590, etc." — Zahlreiche Abweichungswerthe sind darin eingezeichnet ;
mir noch unbekaraite konnte ich nicht unter ihnen finden.
VVeiter eine Notiz : "En 1626 Herbert marque 16 degr. N. W. de Decl.
a 1' embouchure de la Riv. 1' Indus. II y avait alors 20% degr. a Ispahan."
Ebenso: "Moscou, Ferguarson m'a dit y avoir observe* exactment la decli-
naison de 1* aiguille aimantee et l'y avoir trouve*e en 1706 de 7°o' a
l'ouest, T7i4de8° 24V
7. Jens Munck. Danish Arctic Expedition, Hackluyt, Soc. Th. 11 6*.
Im Journal liest man (wahrend der Ueberwinterung bei Port Churchill*
in der Hudson's Bai) :
12. Nov. 1 619. Sonnenuntergang S. W. g. W.
11. Marz 1620. "In those quarters the sun rose in the East South
East and set in the West North West at 7 o'clock in the evening, but it
was not really more than six o'clock on account of the variation."
Der Commentator bemerkt, wie es bei 2 Strichen N. W. 6" 45" hatte
sein sollen. Den Sonnenuntergang vom 12. Nov. behandelt er nicht;
diese Beobachtung liefert 8° 35' N. W. Weil Luke Fox im Jahre 1631
1 7 30' N. W. fand, (die Sacular- Variation fur diese Gegend ist so gut
wie unbekannt) so kommt mir 2 Striche N. W., wahrscheinlich vor;
schliesslich bleibt aber leider die ganze Angabe unsicher.
8. Admiral Beau lieu, 1619 nach Ost-fndien und zuriick. Thevenot,
"Relation de div. Voyages cur. Paris 1664." T. II. Das Logbuch ent-
halt zahlreiche Beobachtungen.
9. In John Harris, Navigantium atque Itinerantium Bibliotheca 1705,
findet man auf pg. 610 die Reisebeschreibung von John Wood nach
Novaja Zemblja, welche zwei sehr interessante Beobachtungen enthalt.
1676. 7V N. W. 69°5o / N. Br. is°i(/ O. v. Gr.
13 ° " 74 3° " 54 3° " Ka P Speedill.
10. Die Journale von Reisen nach Amerika und dent Stillen Ocean urn
das Jahr 1700 \ welche im Depot de la Marine in Paris aufbewahrt werden,
lieferten einige Hunderte hochst interessanten Beobachtungen. Ausser
den auf dem Schiffe St Antoine angestellten, welche mir friiher zuge-
schickt worden sind, fanden sich- unter jenen Reisen sechs Durchquerun-
gen des grossen Oceans vor. Die Reisen sind folgende :
1689 Sr. de la Caff re nach Canada.
1692 Chev. de pidoigne nach Neufundland.
1695 La Mutine nach Canada.
1699 La Badine bei Cuba.
1703 ? nach Peru.
1706 de Boisloree nach Peru.
1707 Hubert von Conception direct nach dem Kap der
Guten Hoffnung.
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48 INTERNATIONAL CONFERENCE [vol. in, No i.j
1 710 de Moncourant von Peru nach China.
1 7 10 Duboccage via Chili nach China und zuriick.
171 1 La Princesse von Chili nach China.
171 1 Brunet von Peru nach den Philippines
17 12 Frezier nach Peru.
1 7 13 Gar din nach Chili.
1 7 16 Bevin von Peru nach China.
1718 Benard de la Harpe. nach Louisiana.
W. VAN BEMMELEN.
INTERNATIONAL CONFERENCE ON TERRESTRIAL MAGNET-
ISM AND ATMOSPHERIC ELECTRICITY.
As the Journal is passing through the press, a printed announce-
ment is received from Prof. A. W. Riicker, President of the Permanent
Committee on Terrestrial Magnetism and Atmospheric Electricity, of
the International Meteorological Congress, that arrangements have been
completed for an International Conference on Terrestrial Magnetism
and Atmospheric Electricity, to be held in connection with the meeting
of the British Association at Bristol, Eng., September 7-14, 1898.
This Committee, consisting of Messrs. Riicker, President; Bauer, von
Bezold, Capello, Carlheim-Gyllenskjold, Eschenhagen, Liznar, Mascart,
Mendenhall, Moureaux, Palazzo, Paulsen, van Rijckevorsel, Rykatcheff,
Schmidt (Gotha), and Schuster, has decided to hold this Conference,
in order that, before reporting upon the various questions submitted to
it by the Meteorological Conference, they may be discussed by a larger
body of persons interested in such subjects. A list of these questions
is given below:
1. In calculating monthly means, all days are to be taken into consider-
ation. It is desirable to give, in addition, means calculated without taking
disturbed days into account.
2. It is desirable to publish the monthly means of the components X, V,
Z, and at least for the months of January and July; the differences £\X,
A y% l\Z* of the monthly means, from the preceding means.
3. It is desirable, for the progress of Terrestrial Magnetism, that tempo-
rary observatories should be installed in certain localities, especially in trop-
ical countries.
The examination of this question was referred to the Committee, which
was requested to point out the spots where these temporary observatories
should be established.
4. On the relative advantages of long and short magnets.
Though the matter of first importance will be the discussion of these
questions, opportunity will be given for papers and communications on
allied subjects. Attendance at the Conference is invited by the Perma-
nent Committee, and by the Council of the British Association for the
Advancement of Science. This is the first opportunity offered to the
magneticians of the different countries for personal intercourse, — one
that will undoubtedly be appreciated by all, and attended with much
good.
Further details will be given in a future number.
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Volume III
Terrestrial Magnetism, yune, 1898.
UEBER EINE METHODE, DIE RICHTUNG ELECTRI-
SCHER VERTICALSTROME IN DER ATMO-
SPHAERE DURCH LUFTELECTRISCHE
BEOBACHTUNGEN ZU BESTIMMEN. 1
Von T. Er^STER und H. Geitel.
In neuerer Zeit ist von verschiedenen Seiten die Moglichkeit
erwogen worden, ob ein Bruchteil der magnetischen Kraft der Erde
auf die Wirkung electrischer Strome zuriickzufiihren sei, die von
der Oberflache der Erde in die Atmosphare und umgekehrt fliessen.
Die Existenz solcher Strome wiirde, — ein nach Genauigkeit und
geographischer Vollstandigkeit ausreichendes Material erdmagneti-
scher Beobachtungen vorausgesetzt — in einfacher Weise daraus
erschlossen werden konnen, dass das Linien-Integral der magne-
tischen Kraft an der Erdoberflache langs geschlossener Curven
einen von Null verschiedenen Wert haben miisste. Die auf Grund
des vorhandenen Beobachtungsmateriales sowohl fur die ganze
Erde, wie auch die unter Verwertung der Ergebnisse der magne-
tischen Aufnahmen von eng begranzten Gebieten fur diese allein
angestellten Berechnungen sind der Annahme solcher electrischer
Verticalstrome im allgemeinen nicht iingiinstig, doch machen die
Berechner z. T. selbst darauf aufmerksam, wie unsicher bei dem
geringen Betrage der gefundenen Stromintensitaten deren Existenz
begriindet ist 2 .
Auf jeden Fall ist die angeregte Frage von grosstem Interesse,
und zwar nicht nur wegen ihrer Bedeutung fur die Theorie des
Erdmagnetismus, sondern nicht minder wegen ihres Zusammen-
hanges mit der der atmospharischen Electricitat. Beriihrt sie doch
gerade einen vielfach discutierten Vorgang, der bei den Erschei-
nungen der Luftelectricitat ohne Zweifel von besonderer Wichtig-
1 Eine kurze Mitteilung iiber diesen Gegenstand i3t in dem Sitzungsberichte des
Vereins fur Naturwissenschaflen zu Braunschweig vom 20. Januar 1898 er-
schienen.
* Eine eingehende kritische Darstellung des jetzigen Standes der Frage auf
Grund eigener Porschungen, sowie derjenigen von A. Schmidt, L. A. Bauer, Carl-
heim-Gyllenskold, van Rjrckevorsel und von Bezold giebt Herr A. Rucker in "Rede
Lecture'* Nature, 57 p., 160, 1897.
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5 o /. ELSTER UND H. GEITEL IVol. hi, no. 2]
keit ist, namlich den Electricitatsaustausch zwischen dem leitenden
Erdboden und der Atmosphare. Dass ein solcher stattfinden muss,
schliesst man aus der einen Thatsache, dass die Erdoberflache im
allgemeinen electrisch geladen ist, in Verbindung mit der andern,
dass ein geladener Korper an die ihn umgebende Luft Electricitat
abgiebt.
Mogen wir nun dabei den gasfbrmigen Bestandteilen der
Atmosphare ein, wenn auch nur sehr kleines, electrisches Lei-
tungsvermogen zuschreiben oder annehmen, dass staubfbrmige in
der Luft schwebende Korperchen durch Beriihrung mit dem leiten-
den Erdkorper von ihm eine Ladung empfangen, in keinem von
beiden Fallen wird es moglich sein, dass das Vorzeichen der so in
die Atmosphare eingedrungenen Electricitat entgegengesetzt dem
Vorzeichen der electrischen Schicht ist, die den Erdboden bedeckt.
Die Richtung eines etwa vorhandenen electrischen Verticalstromes
ist daher, soweit dieser von der Erdoberflache aus durch einen der Elec-
tricitat szerstreuung oder der Leitung analogen Vorgang bedingt
wird, durch das Vorzeichen der Bodenelectricitat vollstandig be-
stimmt. Das letztere ergiebt sich aber bekanntlich ohne weiteres
aus dem der electrischen Potentialdifferenz zwischen der Atmo-
sphare und der Erde; ist diese positiv, d. h. das Potential der Luft
am Beobachtungsort hoher als das der Erde, so ist die Erdober-
flache mit negativer, im entgegengesetzten Falle mit positiver
Electricitat geladen
Diejenigen Flachen der Erde, iiber denen negatives Potential-
gefalle herrscht, wiirden unter der oben gemachten Einschrankung
die Gebiete mit aufsteigendem Verticalstrome sein, der an den
Orten positiven Gefalles wieder zur Erde zuriickkehren wiirde.
Dass die Bahnen der Strome, ihre Existenz vorausgesetzt, ge-
schlossen sein miissen, folgt schon daraus, dass der Erdkorper im
Laufe der Zeit seinen electrischen Zustand im ganzen bewahrt.
Wiirde es nun ausfiihrbar sein, an zahlreichen Stellen einer
mehrere Quadratgrade einschliessenden Curve gleichzeitige Mes-
sungen der Intensitat und Richtung der erdmagnetischen Kraft
vorzunehmen und wahrend derselben Zeit durch luftelectrische
Beobachtungen im Innern der von der Curve begranzten Flache
die Gewissheit zu erlangen, dass wahrend der magnetischen Mes-
sungen das Potentialgefalle der atmospharischen Electricitat im
ganzen Gebiet von gleichem und constantem Zeichen gewesen ist,
so miisste bei einer auf Leitung beruhenden Electricitatsbewegung
die aus den magnetischen Messungen abgeleitete Richtung des an-
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ELECTRISCHE VERTICALSTROME 5I
genommenen Verticalstromes mit der durch das Vorzeichen des
Potentialgefalles bestimmten zusammenfallen. — Leider lasst
sich die angedeutete Methode, die magnetischen Beobachtun-
gen durch die electrischen zu controlieren, nur in eingeschrankter
Weise verwenden. Da das negative Potentialgefalle der atmo-
spharischen Electricitat erfahrungsmassig nur auf kleineren Ge-
bieten, namlich mit dem positiven abwechselnd in Verbindung mit
Niederschlagen aufzutreten pflegt, ausserdem auch nicht von lin-
gerer Dauer ist, so erscbeint es aussichtslos. ein gleichmassig nega-
tives Getalle iiber einer ausgedehnten Flache abwarten zu wollen ;
es bleibt demnach nur die Beobachtung bei positiver Luftelectrici-
tat iibrig.
In diesem Falle wiirde man nun den grossen Vorteil haben, dass
bei guter Wahl der Beobachtungszeit sowohl von der Forderung
der absoluten Gleichzeitigkeit der Messungen abgewichen, wie
auch die Zahl der electrischen Beobachtungsstationen im Innern
der Curve ermassigt werden kann. Bei anticyclonarer Wetterlage
und heiterem Himmel ist namlich das Potentialgefalle mit grosser
Sicherheit als positiv anzunehmen und es wiirden electrische
Beobachtungen von wenigen Orten voraussichtlich geniigen, eine
etwa wider Erwarten eintretende Zeichenanomalie zu entdecken.
Zugleich hat man die gegriindete Aussicht, dass, solange der Wet-
tercharacter derselbe bleibt, auch ein Wechsel zu negativen Wer-
ten nicht vorkommen wird. Daher wiirde man den Spielraum
eines, in giinstigen Fallen von constanter Wetterlage wohl auch
mehrerer Tage fur die magnetischen Messungen zulassen diirfen.
Wie schon bemerkt, ware zu erwarten, dass unter diesen Urn-
standen die gefundene Richtung des Verticalstromes die von oben
nach unten verlaufende ware.
Die Voraussetzung fur das vorgeschlagene Verfahren ist, dass
die Electricitatsbewegung in der Luft der Richtung des iiber der
Erdoberflache herrschenden electrostatischen Feldes folgt.
Nun sind allerdings auch Falle denkbar, in denen diese An-
nahme nicht zutrifft, in denen durch Aufwand irgend welcher vor-
handenen Energie ein Electricitatstransport entgegen den Kraften
dieses Feldes erzwungen wird. So konnen sehr wohl Niederschlags-
teilchen, wahrend sie negativ geladen sind, auf den bei positivem
Potentialgefalle gleichnamig electrisirten Erdboden herabfallen,
also unter Verbrauch eines Teils ihrer kinetischen Energie die Po-
tentialdifferenz zwischen der Atmosphare und der Erde erhohen.
Diese Electricitatsbewegung fallt nicht unter den Begriff der Lei-
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5 2 / ELSTER UND H. GEITEL [vol. in, No. 2]
tung, ihre Richtung ist durch das Vorzeichen des Potentialgefalles
nicht bestimmt. Stammt die electrische Ladung der fallenden
Teilchen von Orten ausserhalb des Integrationsweges, so konnen
auf diese Weise geschlossene Strombahnen zu Stande kommen,
deren magnetische Wirkungen bei der Integration sich nicht com-
pensieren.
Halt man indessen an der schon oben angegebenen Beschran-
kung fest, dass die simultanen magnetischen und electrischen
Beobachtungen nur dann, wenn sie bei heiterem Himmel erhalten
sind, zur gegenseitigen Controle verwendet werden, so fallt diese
Schwierigkeit von selbst fort.
Es ware schliesslich noch moglich, dass auch bei heiterem Him-
mel Energiequellen thatig sind, die in noch unbekannter Weise
eine der normalen Leitung entgegengesetzte Electricitatsbewegung
von der Erdoberflache aus bewirkten. Bis jetzt sind experimen-
telle Grundlagen fur die Annahme solcher allgemein verbreiteten
electromotorischen Krafte an der Grenze zwischen der Luft und
dem festen Erdkorper nicht bekannt geworden und es empfiehlt
sich daher, die Frage nach ihrer Existenz vorlaufig noch zuriick-
zustellen und zuerst die oben aufgeworfene einfachere in Angriff
zu nehmen : "Stimmt die Richtung der aus erdmagnetischen Beob-
achtungen zu erschliessenden electrischen Verticalstrome in der At-
mosphare unter der Annahme eines gewissen Leitungsvermogens
der Luft mit der aus dem Vorzeichen des electrischen Potent ial-
"gefalles auf der in Betracht gezogenen Flache abzuleitenden iiber-
ein und zwar unter Beschrankung auf das normale positive Ge-
falle bei heiterem Himmel ?" Gesetzt, es stellte sich die zu erwar-
tende Uebereinstimmung der Stromrichtungen bei wiederholten
Beobachtungen immer wieder heraus, so ware damit die reale
Existenz der electrischen Verticalstrome hochst wahrscheinlich
gemacht.
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THE ALTITUDE OF THE AURORA ABOVE THE
EARTH'S SURFACE.
By Professor Cleveland Abbe.
(Continued from March number.)
Dai/ton. — In the first edition of his Essays, 1 pages 69 and 70,
Dalton says that, from observations 2 by himself at Kendal and by
Crosthwaite at Keswick, distant 22 miles, at right angles to the ob-
served arch, the altitudes of the edge of the arch being respect-
ively 53 and 48 , the computed altitude by the parallax method
was 150 English miles. An error of 2 ° in either altitude, which
exceeds the bounds of probability, would give 83 or 750 miles re-
spectively. In his preface he shows that his ideas of the aurora are
original, although partly the same as those of previous authors.
He finds that the beams of the aurora borealis are governed by the
earth's magnetism, but notes that this idea had been conjectured by
Mr. George Birbeck, of Settle, Yorkshire, and that it had also been
more fully expounded by Halley. He rejects, as extravagant,
Mairan's idea that the aurora is a form of zodiacal light. At page
72 the altitude of the aurora of March 30, 1793, is determined from
two observations, viz. : At Keswick, at 8:35 P. M. — while the lower
edge of the arch was 14 above the north horizon Crosthwaite
observed that vertical streamers reached past the zenith 43 ° to-
ward the south. At Kendal (north 54 17', and about 17 miles mag-
netically south of Keswick), Dalton observed the aurora 30 past
the zenith at 8:40 P. M. Assuming these two observations to be
simultaneous, and to refer to the lower extremities of the beams,
the parallactic method gives an altitude of 62 English miles.
At page 153, Dalton gives his original views as to the nature
and structure of the aurora. Having concluded that the auroral
beams owe their apparent curvature and convergence to the illu-
sions of perspective, and that they must in reality be straight beams
parallel to each other, nearly perpendicular to the horizon and
cylindrical, he further concluded that the density to the northward
and toward the horizon, as well as the thinness about the zenith, is
» Meteorological Observations and Essays. First Edition, London, 1793. Second
Edition, Manchester, 1834.
3 Made on February 15, 1893.
2
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54 CLEVELAND ABBE [Vol. in, No. a.]
also a perspective effect. As the tops of the beams appear to rise
above each other in regular succession, he concluded that they are
all of the same length and height, and that the greatest angle sub-
tended by the vertical beams enables us to determine the propor-
tion of their length to their height above the earth's surface.
Finally, the great aurora of 1792, October 13th, led him to the dis-
covery of the relation between it and the earth's magnetism. He
found that the grand dome of auroral light was evenly divided by
the plane of the magnetic meridian, and that a line drawn to the
vertex of the dome pointed in the direction of the dipping-needle,
whence it followed that the luminous beams were all parallel to that
needle, and that other auroras had always presented the same paral-
lelisms. Consequently the beams were guided, not by»gravity, but
by the earth's magnetism. Corresponding observations subse--
quently made by Mr. Crosthwaite, at the request of Dalton, confirmed
these conclusions. The altitude of the aurora rests upon the ob-
servations of 1793, February 15th and March 30th. The similar
views of H. Cavendish as to the perspective illusions, as presented
to the Philosophical Society in 1790, were not then known to
Dalton. He classifies the auroral phenomena into :
1. Horizontal light, like the twilight.
2. Slender luminous beams of dense light continuing from 10 to 60 sec-
onds, often with a quick lateral motion.
3. Flashes pointing upward like the beams, but broader and more diffuse,
sometimes continuing for hours.
4. Arches like rainbows, which frequently cross the heavens between op-
posite points in the heavens. When an aurora takes place the phenomena
succeed in the following order : {a) Faint rainbow arches ; (b) Slender beams ;
(c) The broad flashes ; (d) The horizontal northern light, which is simply the
blending of an abundance of flashes and beams. The beams are arcs of great
circles, with the observer at the center, and, if prolonged, all intersect at one
point.
The rainbow arches cross the magnetic meridian at right angles ; if sev-
eral appear, they are concentric and tend to the magnetic east and west
[The preceding generalizations agree entirely with all earlier observations
of auroras quoted by Dalton. C. A.]
The beams converge to the south pole of the dipping-needle.
The angle subtended by the length of each beam is not the same, but is
a maximum about half way between the horizon and the zenith ; the beams to
the southward subtend smaller angles than those to the north, having the same
altitude.
Every beam is broadest at the base and tapers upward ; but it comes to a
point before the continuation of its boundary lines meets in the common
coronal center.
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THE ALTITUDE OF THE AURORA 55
The luminous beams are cylindrical and parallel, at least over a moderate
extent of country.
These cylindrical beams are all magnetic and parallel to the dipping-
needle.
The height of the rainbow-like arches was about 150 English miles on
February 15, 1793, or, as calculated by Mr. Cavendish, between 52 and 71 miles
on February 23, 1784.
The beams of the aurora are similar and of equal dimensions.
The bases of the beams are at a distance above the earth's surface nearly
equal to the length of the beams, which latter, on March 30, 1793, seemed to
be 60 or 70 miles, so that the summits were 150 to J20 miles high.
The horizontal light near the horizon is the blended lights of a group of
beams or flashes.
In the second edition, page 227, Dalton says that " there may be
some excuse for persons who think the height of the aurora to be
anything between 1,000 miles and 1,000 feet." This may be a sly
hit at Espy, whose criticism of Dalton was published in 1833-34.
The aurora of March 29, 1826, was observed over England and Scot-
land, and Dalton's result (altitude 100 miles) was published in the
Phil. Trans., 1828.
On page 240, of this second edition, Dalton says :
The aurora consists of luminous arches or rings, drawn round the mag-
netic poles, in the manner of parallels of latitude around the poles of the earth
on a terrestrial globe, and of luminous beams arising from them or amongst
them, nearly perpendicular to the surface of the earth, or rather parallel to
the dipping-needle at the subjacent places. These concentric arches extend
to 20 , sometimes 30 , but very rarely to 40 from the magnetic poles ; thus the
aurora is seldom seen to the south, in Iceland, which is about 25 degrees from
the magnetic north pole ; still more rarely in the Orkney and Shetland Islands,
which are 35 from the poles ; and very rarely over the middle of Great Britain
and Ireland, which is nearly 40 from the pole ; thus, in the list recently given
of one hundred and eighty-four aurorse, only five or six arches were seen to
pass the zenith in this country. Aurorse are more numerous in the State of
New York than in Britain, because that State is only 30 from the magnetic
pole. This fact shows that the latitude, or distance from the equator, is not the
regulating principle of the aurora, as no aurora has ever been seen, that I am
aware of, in Europe, on the parallel of New York. In the years 1828 and 1830,
there were one hundred and two appearances of the aurora in the State of
New York ; in this country we have registered only forty-two.
As auroral arches are seen in Great Britain, Ireland, and America at the
same time (page 221, September 29th), it may be presumed the arch extends
sometimes uninterruptedly from Europe to America. If the arch be one
hundred and fifty miles high, its visible extent at any one place, from the
eastern horizon to the western, will be one thousand eight hundred miles
(see page 166). Hence, if an arch is seen from the west of Ireland to descend
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56 CLEVELAND ABBE [Vol. in, No. 2.]
to the west horizon, and from New York to descend to the east horizon, the
parties will see % of their distance covered by the arch.
When it is considered that the Icelanders usually see the aurora to the
north, and we in Britain on the same magnetic meridian, but further from
the pole, see the same aurora to the north, it is an unanswerable argument
for its great elevation. If the summits of the beams of the aurora be three
hundred miles above the earth in Iceland, they will be visible at Paris (page
166) ; and in Iceland, if the aurora extends 5 beyond the zenith to the south,
it may still be characterized there as an aurora borealis or northern lights,
as the probability will be that more than three-fourths of the illumination
will be derived from the northern half of the hemisphere.
Farquharson. — Mr. Farquharson published his ideas in the
Phil. Trans, for 1829 and in the Edinburgh Philosophical Journal,
April, 1823, VIII, page 303. He believed that the aurora is not more
distant than the mass of clouds through which it is observed, and
the aurora of 1825, November 22d, seemed to him decisive of the
question.
Parry. — Captain Parry at Port Bowen, 73 N., 89 W., with Lieu-
tenant Sherer, 1 saw the aurora of January 27, 1825, only a short
distance above the land and shooting down between them and it ; and
again, September 20, 1825, saw the aurora appearing to be very
close to the ship (Dalton discredits Parry's observations and con-
clusions).
Thomson. — Dr. Thomson (see Vol. IV. p. 429 of his "Annals
of Philosophy," London, 1814), according to Capron (see his " Au-
rora, " p. 83), concluded from the observations of Mr. Cavendish
and Mr. Dalton that the arched appearance of the aurora was merely
an optical deception and that in reality the arch consisted of a great
number of straight cylinders parallel to each other and to the dip-
ping-needle at the place where they were seen.
We have here three distinct conceptions, — (1) That the arch con-
sists of short columns of light in close proximity and all parallel to
the free needle ; Thomson says " at the place where they were seen ;"
but as the arch extends over many miles east and west, it is likely
that he intended to refer to the dipping-needle at each point along
the arch and not at the place where the observer is located. (2) If
the arch were really straight, it would appear, by the elementary
rules of perspective, as a curved line arching the sky from one side
of the horizon to the other. (3) If the individual columns are suffi-
ciently close together, the arch would appear as a uniform band of
iSee his Journal of the Third Voyage, pp. 61-170.
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THE ALTITUDE OF THE AURORA
57
light ; but if they are scattered irregularly, the arch would appear
as a curtain of disjointed bright columns.
There are thus three forms of perspective illusions, in addition
to the formation of a corona by perspective, which was first pointed
out by Halley.
Muncke. — In his article on the aurora, in the new edition of
Gehler's Physikalisches Worterbuch, published in 1833, Vol. VII,
pages 159-175, Muncke reviews the computations of the height of
the aurora. He gives full credence to the observations of those
who have seen the auroral light in and below the clouds, and
declares his disbelief in the results of the calculations that give it a
great altitude. Muschenbroeck had arrived at the same conclusion
a century before. Muncke declares that the apparent intensity in
brightness at different points of an arch, or the same point seen by
observers at different distances, is entirely incompatible with the
idea that all see the same luminous body.
Espy. — In the Journal of the Franklin Institute for July, 1833,
Vol. XII, page 5, Professor A. D. Bache communicates the observa-
tions of James P. Espy on the aurora of 1833, May 17th, in which
Espy says: "The dew-point has risen 12 Fahr. since the preced-
ing day. It is highly probable that an upper current (not the up-
permost) of air was moving in the direction in which the arch
moved, as the air had been moving in that direction a few hours
before; and I have frequently observed, when the wind changes,
the lower strata near the earth change first. From the 10th until
the afternoon of the 15th of May the wind had constantly been, by
day and night, almost exactly south, with a high dew-point, carry-
ing an immense quantity of vapor to the north ; on the evening
of the 15th, and until the night of the 16th, the wind was N.E.,
with rain; and on the morning of the 17th the wind was north."
A more complete statement of Espy's theory as to the connec-
tion between the auroral arch and the superposed layers of moist
and dry air, was subsequently given by him in the same journal. 1
In some remarks, page 294, on the circulation of the atmosphere
and the currents produced by the evolution of caloric when cloud
or rain is formed, Professor Espy says :
There is sometimes a middle current moving in a direction different
from the other two. . . . When a middle current occurs, I have frequently
observed that it is in consequence of a change of air — the lower strata of air
'James p. 'Espy, Journal 0/ the Franklin Institute, Nov., 1833, Vol. XII., p. 294.
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5 8 CLEVELAND ABBE ivol. hi, no. a.j
beginning to change first. Whether this is always the case, I am not pre-
pared to say. Such a coincidence of circumstances appears to me very favor-
able to the production of an aurora boreal is.
Suppose the air in motion for some days from the north towards the
south, or anywhere near that direction, bringing with it a low dew-point;
suppose the air below suddenly to change round and blow from the south, or
nearly so, towards the north, bringing with it a high dew-point, whilst a mid-
dle current is still blowing from the north. When the upper current, with
its low dew-point, overlaps the lowest current, with its high dew-point, the
vapor in the lowest current shoots itself up by its own elasticity into the up-
per and colder current, and either by forming a better conductor than ex-
isted there before, permits the transmission of electricity from one current
to the other, or else, by condensing in the colder current, gives out elec-
tricity. In the latter case, clouds would certainly be formed ; in the former,
they might or might not This hypothesis requires the confirmation of re-
peated observations. I have seen but three auroras since I conceived the
hypothesis, and all the phenomena observed in these were highly favorable
to it
It is now a point well established that the aurora is in the region of
the clouds, sometimes not a mile high, and on the night of the 17th of May,
1833, the motion of the beautiful arch of light towards the south was ex-
actly equal to the motion of the clouds in the same direction — all the heav-
ens north of the arch being cloudy and all south being clear.
This aurora moved south about seventy degrees in an hour and a quarter,
forming a brilliant arch as it approached near the zenith, and disappeared,
about fifteen minutes after ten o'clock, about eleven degrees south of the
brilliant star in Lyra.
Now if my hypothesis is correct, this arch was seen north of Philadel-
phia at an earlier hour, and south of Philadelphia at a later hour. If any
observer has taken a note of the time when the arch was formed and disap-
peared, either to the north or south of Philadelphia, I hope he will be in-
duced by these remarks to send his observations for publication in the
Journal.
Espy next advances an hypothesis with regard to the aurora
and the computations of Dalton. 1 He analyzes the observations on
which Dalton based his computation, and shows conclusively that
Dalton's mistake consisted "in taking it for granted that it was
one and the same arch that was seen at different places in Great
Britain on the 29th of March, 1826." He shows that there were
various arches visible at various places, and that, for instance, the
arch observed at Warrington was not seen as an arch at Manchester,
only four miles distant to the south. He also investigates the au-
rora of February 23, 1784, computed by Cavendish, and shows
that here again two different arches were seen at the two stations,
1 Journal of the Franklin Institute, May, 1834, Vol. XIII, pp. 294, 363.
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THE ALTITUDE OF THE AURORA
59
Kensington and Cambridge, and that none of these were five miles
high. Similarly, the aurora of 1831, January 7th, at Gosport, is
shown to be exceedingly near the earth. He quotes Dr. Brewster's
observation at Edinburgh, 1801, December 5th; Dr. Gister, as
quoted by Wargentin ; Professor Hansteen and many other Euro-
pean authorities, as well as Captain Franklin and Captain Parry in
the polar regions. Finally, he shows that the arches of 1833, May
17th, at Saratoga and Philadelphia, and those of 1833, March 21st,
at Edinburgh and Armagh, were at each station different from those
observed at the other. In general, he concludes, page 370, "I
have demonstrated that the aurora is from one to three miles high,
and as it has always been accompanied by a certain change of dew-
point, ... I am justified in saying that the plausibility of the
hypothesis that was formerly advanced to account for the aurora is
much increased." 1
Twining and Olmstead. — Mr. Alexander C. Twining 2 calcu-
lates the height of several auroras, as follows:
1. December 10, 1835, from observations at New Britain and New Haven,
Conn., the stations being twenty-six miles apart, the resulting parallax was
ij/j°, the angular elevation at the northern station, io)4 , the distance of the
cloud from New Haven for an assumed parallax of 3 , would have been one
hundred and forty-one miles, and its altitude above the surface of the earth
forty-two miles. For the actual observed parallax the figures become much
larger; but Mr. Twiuing's object was to show that the aurora must be, in
general, in the upper portion of the atmosphere. He states, however, that
the actual distance of the auroral cloud was really too great to give an ap-
preciable parallax, considering the crudeness of the observations. We can
only with safety conclude that the parallax was very small.
2. August 12, 1836, observed from a steamboat near Old Field Point, about
twenty-two miles south of New Haven; similar observations made by
Professor Olmstead at New Haven showed that the appearances of the aurora
at these two places were almost identical. The arch passed nearly overhead
at both stations, and only one arch was seen by either observer. "The com-
bined force of these coincidences amounts to a demonstration of identity.
The observed parallax of 19%° gave a height of sixty miles above the earth's
surface, but the parallax appears to have been continually diminishing; for
the vertex as seen at the northern station was stationary, while as seen by me
at the southern station it was constantly and progressively changing south-
ward, which compels us to suppose that the arch had a rapid upward motion
in the vertical of the northern station. This motion reduced the final paral-
1 These views of Espy were favorably indorsed by A. D. Bache in some remarks
suggested by Professor Lesley's communications, and printed in the Proc. Am. Phil.
Sot.. 1862, Vol. IX, p. 63.
1 Am. Jour. Set., Oct., 1837, XXXII, pp. 217-229.
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5o CLEVELAND ABBE [vol. hi, no. a.]
lax to about 8^°, and increased the final height to 144K . This arcn was
narrow, not more than 3 in apparent breadth, and was visible at the extrem-
ities not quite down to the horizon, so that its width • must have been about
three miles, its length seven hundred miles in the first position and eleven
hundred miles in its last or highest position."
3. The auroral arch of May 8, 1836, was observed at New Haven, Meriden,
and Hartford, three equidistant points, in a line bearing north and south.
Each of these observers saw the auroral light spreading southward. The
breadth of the bow was about 12 at New Haven, and not much less at the
other stations. Mr. Twining says : " It is impossible to fix upon a definite
parallax, and though we may approximate to it with entire certainty, . . .
the largest parallax which could be assigned consistently with the observa-
tions would elevate the bow more than one hundred miles. . . . Professor
Olmstead's estimate of one hundred and sixty miles should be esteemed as
the maximum height."
Bra vais and Lottin. — The parallax method was most thor-
oughly tried by the French observers, 1 Bra vais and Lottin, at
Bossekop, Norway, in 1838-39, and again by the Swedish observers
at Cape Thordsen in 1882-83, as we ^ as by Tromholt at Kautokeino,
in combination with the Norwegian station at Bossekop, in 1882-83.
Bravais and Lottin stationed themselves respectively at Jupvig
(lat. 70 6' 8.0") and at Bossekop (lat. 69 58' 3.6"), the distance
apart being 15.62 meters, and the bearing of Jupvig from Bossekop
being N. 15 ° 58' 26" E. A careful examination of the descriptions
of the auroras observed at these two stations, less than ten miles
apart, shows that, in most cases, two expert observers could not
recognize the same features in order to make mutual simultaneous
observations with their theodolites. On page 541, Bravais gives
the parallaxes of well-defined auroral arcs, deduced from the obser-
vations at the two stations, as follows :
PARALLAX
1839, Jan. 12,
a ti
41 <<
(t ((
5h. 37m. 5s.
6h. 2m. 5s.
9h. 30m. 3s.
1 oh. 36m.
-3° 42'
+2 13
+9 52
—0 8
" 21,
it u
K <<
6h. 2m.
7b. 3m.
7h. 32.7m.
—1 34
+1 4
+0 45
In other words, we have here three negative and four positive
parallaxes, showing that in general, for some reason or other, these
observations are not capable of giving any exact information as to
the height of the auroral arc.
Bravais's special method, termed the method of amplitudes,
^ee "Voyages de la Commission Scientifiques du Nord."
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THE ALTITUDE OF THE AURORA 6 1
adopts Hansteen's theory that the arch is a part of a luminous ring,
the points of which are sensibly at the same distance above the sur-
face of the earth, and which surrounds the north magnetic pole in
such a way as to cut at right angles all the magnetic meridians con-
verging towards this pole. Under this assumption we may determine
the altitude by observing at one station both the apparent angular
altitude and the amplitude of the arch, and Bravais adopts the arc
of a circle as approximately representing that portion of the auroral
arch which is visible to any one observer. From 145 determina-
tions of this kind he calculates the altitudes, and concludes in gen-
eral that it exceeds 150 kilometers. (Page 463.) From the rela-
tion between the observed amplitude of the arch and its maximum
altitude, he finds, for 145 arches at Bossekop, the altitude 227 kilo-
meters. (See page 472.) From the breadth of the arch at its
summit, he deduces, for five cases, the average altitude 100 kilo-
meters. (Page 481.)
Bravais states that sometimes the lower end of an auroral beam
seems to be prolonged below the summit of a mountain. This oc-
curred on October 31st and January 2d, and he is almost convinced
that this apparent prolongation was produced by the reflection of
the light on the crystals of snow that covered the mountain. Snow
that has been a long time on the ground is nearly always covered
with crystals of frost. As to auroras appearing between the cloud
and the observer, Bravais saw but one case, and thinks that on that
occasion his eye deceived him. The clouds that are replaced by
auroral light are always cirrus or very thin cirro-stratus. In con-
clusion, Bravais states that while it would seem to result from all
his observations "that the mean altitude of the auroral arc is be-
tween 100 and 150 kilometers, yet, in order to determine the paral-
lax of the aurora more precisely than we have been able to do, it
would be necessary to employ a longer base than ours, say about
100 kilometers in length, and directed as nearly as possible parallel
to the vertical plane through the culmination of the arch. The
two stations, Bossekop and Kautokeino, would satisfy these condi-
tions, and in addition to this would offer to the observers the ad-
vantage of a very free horizon, which is not less important." (See
page 542.) These two stations were subsequently occupied by
the Norwegian observers, and by Tromholt in 1882-83, but, as
we shall see, the results are very different from what Bravais
expects.
Broun. — John Allan Broun, director of the observatory at
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62 CLEVELAND ABBE [Vol. in, No. 2.)
Makerstoun, in publishing his work for 1845 a °d 1846, 1 publishes
three sketches showing the structure of an auroral arch or bow as
seen in the north, which was evidently formed of the lower ex-
tremities of a set of beams parallel to the dipping-needle, and
which, by perspective, apparently converged to the "anti-dip
point ;" that is to say, the magnetic zenith. As these beams
moved from east to west, or vice versa, they appeared perspectively
to be rotating about the magnetic zenith, producing a wave-like
motion from east to west, or opposite to the violent west wind that
was then blowing. This perspective phenomenon is doubtless that
to which Broun alludes in his optical theory of the aurora, as given
in the following paragraph, which is quoted from page lxxxiii of
the same volume:
Although temptations to frame hypotheses have been avoided hitherto, I
can not refrain from repeating here the opinion that the phenomena of the
aurora borealis are chiefly optical. After watching the various phases of the
aurora for some years, the hypothesis of self-luminous beams and arches
appeared to me unsatisfactory, and the strongest argument in its favor — that
obtained from the computed height of the auroral arches— seemed of a very
doubtful character. I was quite prepared, therefore, to adopt the idea — first,
I believe, proposed by M. Morlet to the French Academy in May, 1847— that
the auroral arch is an optical phenomenon of position. M. Morlet has
pointed out that the aich appears generally as a segment of a circle, whereas,
in these latitudes, it ought invariably to appear as the segment of an ellipse,
if the hypothesis be true, of a real luminous ring, with its center on the con-
tinuation of the magnetic pole. He has also, among many other very obvi-
ous objections to that hypothesis, shown that the summit of the arch is gen-
erally in the magnetic meridian of the place, the plane of which rarely
passes through the magnetic pole, and seldom passes through the same point
for three different places. I have, however, felt even more persuaded that
the aurora is, partly at least, an optical phenomenon, from a consideration of
that phase of the aurora constituting the corona borealis, a persuasion that
I stated, in the Literary Gazette of the time, in giving an account of the
beautiful corona of October 24, 1847. Mairan and, more lately, Dalton have
explained this phase of the aurora by an hypothesis of polar beams — long
fiery rods of solar atmosphere, according to the one ; of red-hot ferruginous
particles, according to the other — seen in perspective, as they lie in the direc-
tion of the magnetic force. A little acquaintance with the phenomenon- the
rushing and tilting of the beams against each other, one beam occasionally
rising from the horizon, passing through the center of the crown and beyond
it — would show the improbability of this hypothesis. I am persuaded that
the phenomenon of the corona borealis is produced in a narrow horizontal
stratum of the earth's atmosphere. Thanks to the discoveries of Dr. Fara-
day, we do not now require a ferruginous sea in order to have polarized par-
1 Transactions of the Royal Society of Edinburgh, Vol, XIX, Part ii, p. lxxx.
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THE ALTITUDE OF THE AURORA 63
tides. The watery crystals that inhabit the upper regions of the atmosphere
can themselves assume a polar state, determined by the passage of electric
currents, and we have only to complete this fact by a hypothesis of luminous
electric discharges seen refracted by these crystals, the position of visibility
of the refracted rays depending on the angles of the crystals, and the deflec-
tions from the direction of magnetic force which they suffer by the electric
currents. Such a hypothesis, which occurs at once when an optical phenom-
enon has to be accounted for, would explain these remarkable auroral clouds
so often seen in connection with the aurora itself. It would also serve to ex-
plain the appearance of the arch at certain altitudes, lower for lower alti-
tudes, determined by the position of the source of light, direction of tbe
magnetic force at the place, and the effect of the electric current in deflect-
ing the crystals. The crystals successively deflected by electric currents
would also exhibit the rushing pencils or beams. It need scarcely be re-
marked that differently formed crystals might give rise to different phases of
the phenomenon, while reflection might be combined with refraction in cer-
tain cases, especially in the case of arches seen south of the anti-dip. Such
a hypothesis evidently assumes a source of light independent of these opti-
cal resultants, and the pulsations seen in many aurorse may be real luminos-
ities. It is hazardous, in the present ill-arranged state of auroral observation,
to offer so rude a sketch of a new hypothesis, although we may suffer a con-
siderable defeat in very good company.
Since the previous note was written, I find that M. Morlet has published
a theory of the auroral arch. (Ann, de Ch. y t xxvii, 3me Serie, p. 65.) The
ideas above were stated by me two years ago to different persons.
Morlet. — Morlet, in the memoir above referred to by J. Allan
Broun, elaborates the ideas communicated by him to the Paris
Academy of Sciences in 1847, a °d again in June, 1849. His idea
seems to be that, in general, there is a diffuse electric discharge in
the upper regions of the atmosphere, and that the luminous air
being repelled by the north polar magnetism of fie earth, pushes
southward and, from below, upwards, and that the auroral beams
consist of particles escaping upward by virtue of the magnetic re-
pulsion. (He states that Bberhard at Halle, and Paul Frisi at
Pisa, were the first to propose that the origin of the aurora borealis
is due to atmospheric electricity discharging into a vacuum.) As
to the regular auroral arch stretching east and west as a portion
of the circumference of a small circle of the celestial sphere, he
attributes it to the refraction or the reflection of the general au-
roral light by the small crystals of ice or snow suspended in the
atmosphere; that is to say, the regular or specular, and not the
irregular or diffuse, reflection of light from their surfaces. If a
great number of hexagonal prismatic crystals should exist in any
region, the brilliancy of the specular reflections would overbalance
the diffuse reflection and give rise to beams and arches of light.
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64 CLEVELAND ABBE [vol. in, No. 2.]
If ice-crystals of many shapes are floating in the air, then double
and other complex arcs will be observed, which must have a neces-
sary angular relation to each other, and, as Morlet says, "Future
observations made, under more favorable circumstances, and, by
most exact methods, must decide whether, these relations observed
among the angular radii of the auroral arcs, are laws of nature
or only illusions produced by an arbitrary discussion of quantities
affected by considerable errors of observation." This latter ex-
pression is one full of warnings to every investigator. Nothing
is more common than to obtain deceptive results by applying an
arbitrary formula to observations that are affected by large errors
of observation. %
Walker. — Dr. David Walker, surgeon and naturalist to the
Fox Arctic Exploring Expedition at Port Kennedy, 1858-59, in a
paper presented to the Literary and Philosophical Society of Liver-
pool, January 21, 1861, 1 says:
Electricians and astronomers have endeavored to ascertain the height of
the aurora above the earth, especially by measuring the height of the arc of
the aurora at different places ; but as their observations were taken from dif-
ferent points of view, probably each observer saw his own particular arc, and
the results are, therefore, discordant. Thus, of two observers who calculated
the height of the aurora in January, 1831, one made it eighteen miles, the
other ninety-six.
The ancients supposed the height of the aurora to be very great, even
beyond our atmosphere; but later observers reduced it to seventy- five miles.
Thus, Cavendish supposes its usual elevation to be about seventy-one miles
above the earth, at which elevation the atmosphere must possess but
1 /150000th part of the density of that at the earth's surface. Still more
modern observers think it does not rise above the region of the clouds, and
Wrangel, Struve, Parry, Fisher, and others, ascribe to it a very inconsiderable
height.
Very valuable observations have been made by different persons in Aber-
deenshire, tending to prove that, at times, its height is not more than half a
mile alcove the surface of the earth. Parry, in January 7, 1825, whilst watch-
ing the variations in the form of an aurora, saw a ray of light dart down it
towards the earth, between himself and the land, which was about three
thousand yards from him. This was also witnessed by two of the officers of
the expedition. I believe I am correct in stating that many of the arctic ob-
servers believe the aurora to attain a very inconsiderable elevation in high
latitudes. Hood and Richardson observed the same aurora from different
places. To the one it appeared in the zenith, forming a confused mass of
flashes and beams; to the other, at many miles distant, looking in the same
direction as the first observer, it presented the aspect of a low illu-
mined arch.
'See Proceedings, Vol. XV, page 102-118.
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THE ALTITUDE OF THE AURORA 65
Sir William Hooker informs me that, while passing a night on the sum-
mit of Ben Nevis, he distinctly saw the aurora hanging in the valley between
a neighboring elevation and that upon which he stood ; also that, at another
time, during a fall of snow upon a mountain side, he observed that the par-
ticles were distinctly luminous, the air giving evidence at the same time of
the presence of much free electricity. General Sabine also tells me that he
has seen the aurora low down, and passed through it as one would walk
through a mist On the nights of the 30th and 31st March, 1859, 1 noticed
the aurora between myself and the land. The patches of light could plainly
be seen a few feet above the surface of the water in Bellot Straits, the oppo-
site land being about two and a half or three miles distant ; and I am confi-
dent that if that land had been sufficiently high, the greater number of the
twenty-four auroras seen during the winter of 1858-59 above the water space
in Bellot Straits, if not all, would have been seen suspended at a low eleva-
tion above the water or ice.
Furthermore, on page iu,Dr. Walker adds:
The following remarks embody my ideas on this subject:
At the south of Greenland, where the ice of Davis* Strait edges upon the
waters of the Atlantic, a greater number of auroras is seen than in any other
place along that coast-line. The mass of ice filling up Davis' Strait and Baf-
fin's Bay is broken up by winds, tides, and currents, and spaces of water ap-
pear among the fields of ice. These spaces are recognized through the winter
by the "frost smoke" rising from them. The air in the neighborhood of
these seas is always loaded with extremely minute spiculae of snow. Many of
the auroras noticed were in the direction of the open spaces of water seen
during the day, such spaces being, as usual, marked by the "frost smoke."
I believe these auroras were connected with the vapor arising from the open
spaces of water, and that they were caused by the condensation and subse-
quent freezing of the particles of vapor, such particles evolving positive elec-
tricity, and, by induction from the surrounding atmosphere, producing a light,
transmitted from particle to particle, thus rendering the whole mass of vapor
luminous, the lower edges of the arch of the aurora being the place where
this condensation and congelation first takes place. As the cold increases,
the number and intensity of auroras, seen at any place on the Greenland
coast, are proportionate to the proximity of the edge of the ice to that place.
Loom is. — Professor Elias Loom is, in a series of articles * on
the great auroral exhibition of August 28 to September 4, 1859,
gives the results of a number of calculations as to the height of
the auroral light. For August 28, 1859, at 8.42 P. M., New Haven
time, he finds the lower limit elevated forty-six miles above the
earth's surface, and the southern margin vertical over the parallel
of 38 50' N. The upper limit was 534 miles above the earth's
1 American Journal of Science \ Nov., 1859, to Nov., 1861, 2d series, vols, xxviii
to xxxii.
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66 CLEVELAND ABBE [vol. m, no. 2.)
surface, and its southern margin vertical above the parallel of
36 40' N. For September 2, 1859, at 2 A. M., Havana time, he
finds the lower limit elevated fifty miles above the parallel of
25 15', and the upper limit 495 miles above the parallel of 22 30'.
The aurora of September 2d formed a belt of light encircling the
Northern Hemisphere from latitude 22.5 northward. During
these auroral displays, electric currents of great power were de-
veloped on the telegraph wires, and all observations are consistent
with the supposition that the currents had an average direction
from about northeast to southwest. By comparing the observa-
tions of auroras at Hobart Town, Van Diemen's Land, and other
portions of Australia, with those recorded at Toronto, New York,
and New Haven, he shows that in every instance when an aurora
was observed in Australia, one was seen on the same day in the
Northern Hemisphere. 1
Marsh. — Mr. B. V. Marsh, of Burlington, N. J., calculates the
height of arches and streamers observed during the great aurora of
August 28, 1859, at a number of places in New England and the
Middle Atlantic States.* The calculation assumes that the same
arches and streamers are seen by the observers at all stations. By
combining these stations among themselves in various ways, he
deduces the altitude of the lower portion of the auroral light as
forty-three miles, but the altitude of the tops of the streamers as
596.5 miles, and the width of the arch in a north-south direction
as about 315 miles, extending, namely, from latitude 38 north-
ward to 43 degrees. Mr. Marsh also communicated to the Ameri-
can Philosophical Society of Philadelphia, March 3, 1865, 8 the re-
sults of some calculations of the heights of auroras, which may be
summarized as follows :
1865, January 16. — Observations of the apparent altitude of auroral arches
stretching east and west at German town, Pa. (40 V N. ; 75 n' W., arch 2°.5
to 3°.o wide), compared with observations at Brunswick, Me. (43 53' N. ; 69
55 / W.), where the arch formed two bows, stretching northeast to northwest,
gave 67.3 miles for the height of the arch above the surface of the earth.
1865, February 20. — Arch observed at Newburyport, six or seven degrees
wide, spanning the sky from east to west. Arch seen by Dr. Smallwood at
1 These ideas and computations are but slightly changed in an extended memoir
contributed by him to the Annual Report Smithsonian Inst, for 1865. In this
memoir he rejects as illusions all previous observations by Farquharson, Parry, and
others, that tend to show the lowness of the aurora.
* Journal of the Franklin Institute (3), Vol. XXXVIII, 1859, pp. 353-356.
8 See Proceedings, Vol. X, pp. 24-28.
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THE ALTITUDE OF THE AURORA 67
Montreal, two or three degrees wide, stretching from east to west. Mr.
Marsh calculates the height at 67 miles.
1865, February 21.— Arch, from northwest to northeast, observed by
R. T. Paine at Boston and by H. D. Vail at Philadelphia. Mr. Marsh calcu-
lates the altitude at 64.8 miles at 8:30, Boston time, and again at 66.2 at 8.45.
Mr. Marsh concludes that it is only in auroral displays of the
very first class that the arch or curtain is less than fifty miles
above the earth's surface. Thus, in the grand display of August
28, 1859, the height was forty-three to forty-six miles, and in the
display of September 2, 1859, it was fifty miles.
Lesley. — Professor J. P. Lesley, the distinguished geologist,
defends the conclusion that the auroral light may be very near to
the observer. 1 He believes in the " reliability of the testimony 01
Dr. Walker, Sir William Hooker, and General Sabine, and thinks
it unreasonable that their positive observations should be despot-
ically overridden by the trigonometrical calculations of other stu-
dents." Professor Lesley was located on the northwest side of
Little Glace Bay, not far from its mouth, and seventeen miles
from Sydney, Cape Breton. His graphic words are worth re-
printing :
It was my good fortune to observe an aurora which, to my eyes, was em-
bodied in and swept the earth with successive banks of Cape Breton fog.
On the evening of the 23d of July, 1862, an exclamation of my compan-
ion, who was sitting after tea so as to face the window, looking out towards
the northeast, announced the phenomenon. Going round the house, we saw
what I at once recognized, from the plates of the French expedition to Nor-
way, as a curtain aurora. It was totally unlike any aurora we had ever seen,
and was evidently connected with a dense broadside of fog, which the south
wind had just brought up from the south coast across the Little Glace Bay,
and was driving from us northward. In this fog-bank hung, as it were, a
brilliant curtain of light, with a wide fringe or flounce of maximum brill-
iancy along the bottom edge, the light fading upwards along the curtain, but
traceable to the very zenith, and the curtain stretching from the eastern hori-
zon out at sea to the western horizon on the low hilltops. The perspective
was perfect. The curtain was evidently vertical, thin, straight, long enough
to reach from one limit of the vision to the other, and floating broadside be-
fore the south wind towards the north. No reasoning could convince us that
these were not elements of the phenomenon, and moreover that the lower
edge of the bright fringe was more than one or two hundred yards away, at
its nearest point, when we first saw it. Its rate of departure from us was evi-
dently that of the fog-bank, or that of the gentle south wind then blowing.
1 Proceedings of the American Philosophical Society, for September 19, 1862,
Vol. IX, pp. 60-63.
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6S CLEVELAND ABBE [Vol. hi, no. 2]
The perspective of the whole curtain changed in conformity with that sup-
position. We had both spent our lives in topographical work, and no record
of triangulations made upon this aurora would alter my convictions of the
posture and movements of the beautiful object, derived from the natural tri-
angulations of the unassisted eye.
But this was not all. The two most important features of the exhibition
remain to be described.
In the first place, the curtain hung, not in a perfectly straight plane, but
was magnificently waved or folded in recurrent plaits, like the gophered edge
of an Elizabethan collar; and these folds were confined chiefly to the lower
part of the curtain, or to the flounce of maximum brilliancy, although they
sometimes went up high into the thinner body of the curtain. They were
sufficiently recurved in some instances for us to see through three thicknesses
of the flounce, the fold thus almost tripling its own light. But the perspec-
tive of each fold was unmistakable, and the impression on the mind was that
of the unequal advance of the line of fog-bank, some sectious pushing for-
ward and swinging in front of intermediate sectious which lagged behind.
We saw no material break in the continuity of the light curtain ; nor did
there seem to be any fixed order of curve, the plaits sometimes lying one way
and sometimes another; and therefore no impression of a vortical system was
made, but rather of an irregular advance of the fog-bank. The plates of the
French expedition to Norway ('* Lottin's Aurora Boreal is,") will give a better
idea of the structure of the curtain than any description.
The most imposing part of the scene now followed. We had been watch-
ing the receding curtain perhaps five or ten minutes, and it had reached a
distance of apparently half a mile or a mile (it may have been more, how-
ever, as we had no means of accurate judgment), when we became aware of
the passage over us of a second curtain, which soon occupied the place of the
first, and went floating off after it towards the north, the interval between
them apparently remaining constant, but the brilliancy and definiteness of
the second being inferior to the first. And not long afterwards a third passed
over us, and followed in the rear of the other two, inferior also to the sec-
ond. We gazed with astonishment and delight upon all three together, until
they became an indistinctly defined common aurora in the north. Soon
afterwards the clouds increased, the fog became denser, the light in the
northern heavens was broken by bars and patches of black, and we retired
into the house.
Dall. — Wm. H. Dall, in "Alaska and Its Resources," speaking
of the time when he was in camp at Nulato, latitude N. 64° 40',
W. 1 57 55', on the north and west bank of the Yukon River, from
November, 1866, to March or April, 1867, says, on page 59:
We had entertained great expectations of seeing exhibitions of the au-
rora borealis of unusual beauty, but they were not realized. The few displays
which were observed were of an insignificant character. No colored lights
were noticed, and the brilliancy of the light was far below what we had an-
ticipated. Several of these displays, however, presented phenomena which
may not be uninteresting to the general reader, as showing distinctly some
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THE ALTITUDE OF THE AURORA 69
points not previously established in regard to the mode of appearance of the
aurora under some circumstances. February 11, 1867, an aurora was observed
under the following conditions : From a gap in the hills north of Nulato, a
white light was seen to issue, early in the evening. The sky was much over-
cast with cirro-stratus clouds, which were rapidly passing in a different di-
rection from the wind at the surface of the earth, which last was from the
north. The light before alluded to approached with the wind, at about half
the pace of the wind, in a cloudlike shape or condition, not far from the sur-
face of the earth. The form of this luminous cloud was in successive waves,
or ripples, and resembled the rings of smoke rising from a pipe, one within
another, gradually expanding. The inner or focal rings were more intense
than the outer ones, and the light was more intense in some parts of the
rings than in others. They advanced as the ripples do when a stone is
thrown into still water, and these ripples were compressed in an oval form
by the wind, the longer diameter being east and west, across the current. It
showed unmistakably that the shining medium was in consistence similar to
cloud or mist. From the brighter portions of the rings, light streams of the
same medium occasionally dripped, and dissipated at some distance below
the point whence they originated, from which it might be inferred that the
more intense portion of this medium was denser than the atmosphere. No
rays or streamers issued upwards from the upper edges of the rings, which
were clearly defined and below the real clouds, of which the altitude seemed
less than fifteen hundred feet. The hills from between which the auroral
cloud had issued, and the tops of the higher trees between the fort and the
hills, were dimly seen, or obscured by the lower portion of the haze or
cloud, which seemed not more than a hundred feet above the earth, as seen
from the roof of the higher building. It followed the air- currents entirely,
and all its motions seemed guided or controlled by them. Wavy outlines in
the ripples seemed caused by the differing velocity of the air in different
parts of the current It covered the whole sky in about two hours from the
time of its first appearance. As it spread and enlarged, the light became
fainter. It did not give out a positive light, but had a mildly luminous ap-
pearance, like phosphorescence.
(Note. — These remarkable phenomena were observed, in a greater or
lesser degree, in several instances, an account of which was communicated to
the National Academy of Sciences, at its session in September, 1869, by the
writer.)
Abbe. — The aurora of April 7, 1874, was studied quite care-
fully by myself. 1 All efforts to determine the height of the auroral
light by parallactic methods based on reports from stations a few
miles apart, were rendered nugatory by the demonstrated fact that
at such stations the aurora had, at a given moment, utterly differ-
ent appearances. For some reason or other each observer saw his
own peculiar aurora, and the reports from about one hundred and
1 See my papers in the "Annual Report of the Chief Signal Officer " for 1874,
P. 583 1 »875» PP. 367-374 ; and 1876, pp. 301-335-
4
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70
CLEVELAND ABBE [vol. in, No a.j
fifteen stations confirmed the general conclusion that parallaxes,
properly so-called, were a delusion, and that we must seek to under-
stand the nature of the light and of the optical phenomena before
we attempt to determine its locus. It was evidently not due to re-
flection from the clouds nor to diffraction. Each beam was self-
luminous ; in fact, the whole sky was self-luminous at times, and it
was necessary to conclude that we had here a new form of optical
illusion, such that the locus of a bright auroral beam depends
upon the fact that the line of sight from the observer is tangent,
or nearly tangent, to a bright cylindrical surface of complex curva-
ture. The following items are extracted from page 309 of my
memoir in the " Report" for 1876 :
{a) The auroral light exists sometimes as patches or clouds, but more
frequently as luminous lines inclined to the earth's surface, and approxi-
mately parallel to the free magnetic needle.
(6) These luminous lines are associated together, forming luminous wave
surfaces and cylindric surfaces, either of which appears sharply defined in the
portions where their tangent planes are directed toward the observer, giving
rise to the appearance of beams or streamers, which are, therefore, ill-defined
on one edge, but sharply defined on the other.
{c) The luminous wave surfaces are themselves arranged parallel to each
other, giving rise to arches or belts across the sky, which, when the observer
is favorably situated, are seen by him as striated belts or arches, which struc-
ture is well described by one observer as resembling vertebrae and ribs.
When the luminous lines are quite straight and comparatively short, and
especially when perfectly parallel, but without being grouped into wave sur-
faces, there results the corona seen around the magnetic zenith by such ob-
servers as are properly located.
(d) Inasmuch as the edge of a streamer is simply an optical effect, it fol-
lows that two persons at a distance from each other, viewing the same wave
surface, will perceive two different streamers. Although the auroral light
emanates from definite points and lines, yet the arches and streamers have
no proper locus.
{e) Slight changes in the flexures of the luminous surfaces produce the
changes in the appearances of the arches and beams at any one station.
Therefore the movements of the arches, beams, and striae are quite diverse
from the changes among the luminous lines.
(f) If the motion east or west of waves of light running along the
arches that pass near the zenith is the same as the east and west motions of
beams of light seen when the same arch is observed from a station south of
that arch, then the apparent angular motion observed at the southern station,
compared with the angular motion observed near the zenith of the northern
station, will afford an additional means of determining the average elevation
of the light.
In continuation of the views expressed by me at that time, the
following more explicit paragraph may be quoted from the Monthly
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THE ALTITUDE OF THE AURORA 71
Weather Review for October, 1893, p. 291. Subsequent studies, pub-
lished in the Review for 1894, served to still further establish these
views :
The relation of the aurora to thunderstorms continues as stated by the
editor in connection with the aurora of February 4, 1872, 1 and in the Monthly
Weather Review for 1874, and in his report on the aurora of April 7th of that
year ; viz., that the aurora is most frequent in the northern part of the
country when thunderstorms are more frequent to the southward. An appar-
ent exception to this rule would seem to have occurred on the 1st of October
when the auroras were too few, and on the 14th when they were too numer-
ous, as compared with the number of thunderstorms. Such exceptions may
show the necessity of modifying the rule when the reports of thunderstorms
and auroras have been more thoroughly systematized. As stated at that time,
the aurora is an electrical discharge between masses of air rather than between
the air and the ground, although sometimes the latter may also occur in high
northern latitudes. It is usually confined to a widespread horizontal area at a
very moderate height above the earth as compared with the great heights
that have been usually attributed to it. The layer in which it occurs appar-
ently represents the boundary region between a lower layer of cold, dry air,
and an upper layer of moister air that is overflowing. These conditions are
such as prevail in the northern quadrant of an area of low pressure or on the
southern edge of a high area, at least in latitudes 40 to 6o°, and east of the
Rocky Mountains. The lightning discharge between clouds at low altitudes,
or between them and the earth, requiring, as it does, higher temperatures,
more aqueous vapor, and more rapidly ascending currents, is characteristic
of the areas of low pressure, and especially of the quadrant of southerly
winds, as was then pointed out ; while auroras, requiring lower temperature,
less vapor, and probably spiculae of ice, such as attend the formation of
snow, are characteristic of the upper layers over the region intermediate be-
tween the areas of lowest and highest pressures, and where the ascending air
of the low pressures is spreading horizontally above, while the descending air
of the areas of high pressure is spreading horizontally below.
The meteorological conditions necessary to the production of the auroral
light may be either widespread or local. The principal condition seems to be
the presence of a layer of air in which moisture is condensing into minute
spiculse of ice. This condition prevails over the broad zones around the earth
within 30 of the north and south poles, throughout the greater portion of
the year, and it may possibly prevail in the upper atmosphere throughout
the year much nearer the equator. This condition also prevails, especially on
the northern side of the areas of low pressure, or storm centers, and there-
fore in the easterly quadrant of the areas of high pressure. But notwithstand-
ing this favorable meteorological condition, there can be no aurora without a
special discharge of electricity. The ultimate origin of electrical disturbance
may be either cosmical or terrestrial. If the former, then auroras are subject to
periods of one, eleven, or fifty-five years; but if the latter, and especially in so
far as this disturbance is piezo-electrical, there will be lunar and solar tidal
periods; and there may also be localities of special frequency, such as the au-
> See Proc. Phil. Soc. Wash., Vol I, p. 65.
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72 CLEVELAND ABBE [Vol. hi, no. 2.1
roral zone in northern latitude 55 to 70 . It is thus plain that the aurora de-
pends, on the one hand, on the condition of the atmosphere, and on the
other hand, on the condition of the interior of the earth and the sun. When an
electrical disturbance from the sun, or from the interior of the earth, reaches
the earth's atmosphere, it will produce an auroral light in those portions of
the atmosphere whose conditions are favorable thereto, but not otherwise.
The two conditions must combine in order to produce the auroral effect
Weyprecht. — Views similar to my own, in some respects,
were published almost simultaneously by Weyprecht, in his " Nord-
licht Beobachtungen," as the results of the Austrian-Hungarian
Arctic Expedition, 1872-1874. In this memoir, as read before the
Academy of Sciences at Vienna, May 17, 1877, he says: "If in
the following pages I add one more to the many descriptions of
auroras already existing, it is because the auroras observed by us
at Franz Joseph Land showed great departures as to their general
character from those described elsewhere ; and because, in general,
the phenomenon, as we saw it, is entirely different from that which
is observed in lower latitudes, and which, in many cases, has been
used as a basis for far-reaching conclusions/'
With regard to the altitude, Weyprecht says, on page 14, that
the auroras of northern latitudes, in most cases, appear to the ob-
server to exist at a much lower altitude above the earths surface
than in southern latitudes, but this appearance is mostly due to the
greater intensity of the phenomenon. Not only the brightness is
greater, but the movements are more rapid, and one can not think
that the rapidly-moving rays which flash up towards the magnetic
zenith in a fraction of a second are really at the enormous dis-
tances that result from the direct measurements of auroras. He
quotes Lefroy, Parry, Ross, Franklin, Richardson, Hood, Back, and
Farquarson as indorsing the nearness of the aurora. He discusses
the observations of Bravais and Lottin, who found, for well-defined
arches, three impossible negative parallaxes, and gives them but
little weight as proving the great altitude of the aurora. On the
contrary, he is careful to say, " The simultaneous altitudes of an
aurora at two stations can only be measured with a certain accu-
racy when the phenomenon is so well marked that neither observer
is in doubt as to his having observed the same point as the other,
and this is only possible when the point does not move rapidly."
Weyprecht is evidently still of the opinion that the two observers
are pointing upon the same definite concrete beam of light, and not
upon an optical illusion, such as the rainbow or the center of con-
vergence by perspective of the auroral rays.
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THE ALTITUDE OF THE AURORA 73
In the absence of satisfactory measurements for the determi-
nation of the altitude of the aurora, Weyprecht states that he is
convinced from the phenomena observed by him (1873, February
nth), when the aurora was in or below ,the cirrus clouds, and that of
1874, January 17th, when the aurora was seen between himself and
the clouds, that the following opinion is justified, page 21 : " When
we consider all these matters without prejudice, we can not easily
avoid the conclusion that, in its normal development, the aurora is
in general a phenomenon at a very low altitude, and that its eleva-
tion above the earth increases the further it reaches southward,
and that even in those regions where it shows the greatest inten-
sity and frequency the individual phenomena occur at very differ-
ent altitudes, according to the manner of their appearance."
After the publication of this work, Weyprecht took a leading
part in the preparation for the international polar work of 1882-83,
but unfortunately died before the Austrian expedition sailed. I
quote the following from his last publication on this subject, his
"Praktische Anleitung zur Beobachtung der Polarlichte," pub-
lished in Vienna in 1881, in which he has introduced a few slight
modifications from his previous works.
Weyprecht recognizes the following classification of the form
and structure of aurorae :
1. Bogen, arcs, arches: Nearly regular, analogous to the form of the
rainbow, stretching in general on both sides to the horizon and moving
slowly towards or from the magnetic north or south, or rising and falling to-
wards the zenith.
2. Bander, Bandes, streamers : Frequently irregular in their form, but
always giving the impression of a ribbon moving through the atmosphere, al-
most always curved in pleats and windings, and of much greater extension in
longitude than in latitude. These bands consist of masses of light or individ-
ual rays as long as the width of the band, unequally distributed, directed to-
ward the magnetic zenith close together, and the interspace is filled with
diffuse light This band reaches to the horizon only on one side, or it may
be limited on all sides ; very seldom does it reach the horizon on both sides.
3. Faden, fits, threads : Extremely delicate rays of light of very differ-
ent lengths, sometimes reaching from near the magnetic zenith to near the ho-
rizon, and generally grouped in such a way that they form fan-shaped areas
covering a portion of the sky. These rays do not constitute a continuous
phenomenon, but are separated from each other by dark spaces. Frequently
these fans are the continuation upwards of streamers, which latter then form
the continuous lower edge of the fan.
4. Krone, Couronne, Corona : The union of rays or masses of light at
a common center, always in the neighborhood of the magnetic zenith, and
actuated by a more or less intensive, movement toward or around that
center.
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74 CLEVELAND ABBE [Vol. in, No. a.j
5. Polarlieht, Dunst, Plaques, Haze : Ill-defined accumulations of light
at any point of the sky, without well-defined outlines.
6. Polar licht segment, Segment obscur % dark segment : An apparent dark
circular segment, bounded by a permanent and very low arch of light in the
magnetic north or south. This low arch is generally the starting point of
the arches of Article 1.
7. Polarschein, Lueur polaire, polar shine : The appearance of fire in the
northern sky some distance above the horizon, which is the form in which
the auroral light frequently appears at stations in middle latitudes, but is
rarely, or never, observed at northern stations. The principal characteristic
of this form is, that the rays diverge from the horizon upwards, whereas in
all the other forms, when rays can be distinguished, they converge from the
horizon upwards.
Besides the above, there are transition forms, in which it may be occa-
sionally doubtful to which of these types the phenomenon belongs.
In addition to the forms, we must distinguish the motions ; these are of
two kinds :
(1) The movement of the phenomenon as a whole \ such as the rising
and falling of the streamers and arches with respect to the horizon, the hori-
zontal movement and lengthening and shortening of the threads, the change
of place of the polar haze. These movements do not generally go on so rap-
idly but that they must be determined by a steady inspection of the sky.
Neither can they be determined by comparing the appearances of the sky at
intervals of an hour. In the region of greatest frequency of the aurora, one
does in general not see the same aurora at the end of an hour, but a new
one. It would, therefore, be illusory if one should adopt the change in two
successive hourly observations as the movement that has really taken place
during the hour.
(2) The changes of the light within the aurora may occur in two ways :
{a) IVellen, Ondes, Waves: Waves of light that run along the streamers,
and here and there also the arches, along their entire length, and therefore,
in general, from the magnetic east and west toward the opposite end of the
streamer. These cause a rolling or jumping of the streamers, according as
they consist of indefinite masses of light or of well-defined rays, constituting
the "merry dancers" of the English observers. The movement of the
waves can occasionally appear to run backwards, in which case the arch ap-
pears to form loops or knots. The flickering and the brightening and fading
of individual spots in the threads belong to this form of motion.
(6) Blitze, Dards, Flashes: Short, rather broad rays, that shoot with
great rapidity from the streamers towards the magnetic zenith, or inversely.
These are always the precursors and attendants of brilliant coronas, and es-
pecially occur when a streamer or arch composed of rays dissolves into a
corona.
De la Rue and Miller. — Experiments on the electric dis-
charge in vacuo lead Warren de la Rue and H. W. Miller 1 to the
conclusion that a certain tenuity of atmosphere is necessary for a
display of maximum brilliancy and a certain other greater tenuity
will entirely prevent the discharge. This former limit, or the
pressure of least resistance, is about 0.379 millimeters, and corre-
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THE ALTITUDE OF THE AURORA 75
sponding to this is the elevation of 37.67 miles above sea-level at
which, therefore, the display will be of maximum brilliancy. The
lowest pressure they have produced — namely, 0.000055 millimeters
— corresponds to a height of 81.47 miles, and probably at this height
the discharge would be considerably less brilliant. The pressure
0.00000001 millimeters corresponds to a height of 12,415 miles,
where it is scarcely probable any discharge can occur.
The color of the discharge varies with the tenuity of the air
or other gas, at least around the positive electrode, while the violet
hue is in the neighborhood of the negative electrode. The follow-
ing table shows some of the results of actual observations :
Mm. Pressure Height in miles Remarks
°-379 37-67 Maximum brilliancy.
0.800 33-9^ Pale salmon tint
1.000 32.87 Salmon colored.
1.500 30.86
3.000 27.42 Carmine.
20.660 17.86 "
62.000 12.42 "
118.700 11.58 Full red.
Galle. — In the " Zeitschrift " of the Austrian Meteorological As-
sociation for 1882, Vol. XVII, p. 435, Galle suggests that accurate
observations of the apparent altitudes of auroral arches would be
appropriate for the determination of the altitudes, even if made
at only one place, just as the altitude of the center of the cor-
ona is utilized in Galle's first method. 2 He deduces from ob-
servations of the arc at Breslau and at Berlin, on October 2, 1882,
an approximate altitude of fourteen geographical miles. He also
adds : "After the cessation of this aurora, streaks of cirro-stratus
were observed pointing northward, which moved from the west to-
ward the east, or opposite to the movement of the auroral clouds, and
which, eventually, generally dissolved into cirro-cumuli that were
arranged perpendicular to the direction of the original cirro-stratus
streaks. In general, the cirro-cumuli that often accompany or fol-
low the auroras, form in different portions of the sky."
Galle's first method of computing the height of the auroral
light was as follows :
The observer at B (see Figures 1 and 2) sees the auroral corona
within the patch of light Z,, and measures the zenith distance of its
center in his magnetic meridian. This is the angle R B Z, made with
his vertical by the parallel lines of light that compose the corona.
This observation fixes the location of the light as being somewhere
1 Warren de La Rue and H. W. Miller : On the Height of the Aurora Borealis.
Proc. Roy. Soc. y 1880, Vol. XXX, page 332.
'See Poggendorff Annalen y Vol. 146, or Astronomische Nachrichten, Vol. 79,
No. 1877.
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CLEVELAND ABBE
\ Vol. Ill, No. 2.]
along the line B R. The direction of the free dipping-needle at B gen-
erally differs from that of the line Q B R by a few degrees, and Galle's
assumption is that the latter line agrees with the dipping-needle at the
Z ?
Figure i.
location of the auroral light. He therefore seeks for a point on
the earth's surface, such as G, where the needle is parallel to the line
Q R t and assumes that in the vertical above G there is no important
P
Figure a.
change in the position of the free needle. The differences in mag-
netic latitude between B and G, or the angle B C G t as well as the
angle ZBR t are now known, and it is easy to compute the height GL.
To be continued.
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RESULTS OF PROFESSOR ESCHENHAGEN'S MAGNETIC
INVESTIGATIONS IN THE HARZ MOUNTAINS. 1
By G. R. Putnam.
Under the auspices of two German geographical and geological
societies, Professor Eschenhagen, during the years 1888' and 1890,
made detailed magnetic observations at 42 stations in the Harz
Mountains, which lie about 125 miles southeast of Berlin. Earlier
investigators had noted the fact that the granitic rocks of this re-
gion were sometimes strongly magnetic, but had not gone beyond
the local surface conditions. This work, however, was intended to
develop the more general magnetic anomalies in this region, and
especially their relation to the geological structure, and to the data
furnished by the geodetic surveys as shown by the plumb line de-
flections, indicating certain conditions of the attracting masses be-
neath the surface. An investigation very similar to this was carried
out by Fritsche in the vicinity of Moscow in 1893. 2 The Harz
region is well adapted to research of this character ; for the reason
that magnetic observations have been made in the surrounding por-
tions of Germany from which the normal conditions may be de-
duced; and, further, because these mountains have been studied
geologically, and have also been covered by geodetic triangulation,
from which the plumb line deflections have been computed.
Some description is given of the instruments and methods used.
The observations at a station required about three hours, and in-
cluded sun observations to determine the true meridian ; for the
declination, the difference was read with a magnetometer theodolite
between that meridian and the position of a needle resting on a
pivot, the needle being read both upright and turned over; the
horizontal force was determined relatively by deflecting this magnet
by another placed at a definite distance; the inclination was ob-
tained with the usual dipping-needles. Where sun observations
could not be obtained, the true meridian was sometimes obtained
from geodetically determined directions. The geographical posi-
1 Magnetiache Untersuchungen itn Harz, von Professor Dr. M. Eschenhagen.
Stuttgart : Verlag von J. Bngelhorn. 1898. Forschungen zur deutschen Landes
und Volkskunde. Elfter Band. Heft 1. 8vo. Pages 20, plates 2.
'See Terrestrial Magnetism, Vol. I, No. i, page 50.
5
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78 G. R. PUTNAM [vol. hi, no. 2.}
tions were taken from the general charts. Care was taken to select
stations free from local disturbances, as buildings, etc., and the sur-
face stones were tested to see if they were free from magnetic in-
fluence. The magnetic traveling instruments used, packed in a
portable case, weighed 25 to 30 kilogrammes, and one to two sta-
tions at most were occupied a day. It is stated that the uncertainty
of the results was about 1' for declination, i'.2 for inclination, and
.00010 C. G. S. unit for horizontal intensity.
The effects of regular and irregular diurnal and annual changes
in the magnetic elements were eliminated by comparison with the
continuous records of the nearest fixed magnetic observatories —
those at Wilhelmshaven and Potsdam. The series taken in the two
different years were connected by the common station Clausthal,
and all the results were reduced to the mean epoch 1888.5. Two
stations, showing very considerable local disturbances, were not
included in the discussion. . The magnetic anomalies were deduced
by comparing the observed values with those taken from a chart
on which the general isomagnetic lines had been drawn, based on
observations made throughout the surrounding portions of Ger-
many. From the three observed magnetic elements were then de-
rived the three components of the magnetic force — namely, the
horizontal force in the true meridian, and in an east-west direction,
and the vertical force — and the differences between the chart and
observed values were obtained. The resultants of the first two, or
the anomalies in the horizontal plane, are shown in Chart I for
each station by the arrows, both in direction and magnitude, one
millimeter representing .00003 C. G. S. units. These arrows will
in general be longer the nearer the station is to a disturbing center.
An attraction line, or magnetic ridge line, is drawn on the chart,
extending from Sangerhausen to Herzberg, being a line towards
which the arrows point from adjacent stations on either side. The
position of this line would be more clear if the arrow for Sanger-
hausen had not been omitted. The branch toward Quedlinburg is
not so apparent ; but these ridge lines can be more definitely located
when the anomalies in the vertical force are also considered. These
are shown on Chart I by figures beneath the station, giving the
units in the fifth decimal place, + for observed value in excess.
The condition of the vertical force is also shown by the vertical
ruled lines for areas where it is in excess, and horizontal lines
where it is in defect, the magnitude being shown by the spacing of
the lines. It will be seen that in the greater part of this region
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MAGNETIC ANOMALIES IN HARZ MOUNTAINS 79
fi^ — fr 1 — r+^-Sfl ; JUS MJ J
I f . / -O- lilir Ifjlilli
7vHi ZJ Hlrilli III 1
s^E vt r l ^-f!' flu *IEIf 1j
1 * * if ill HirftitH
Chart I.— Magnetic Anomalies in the Harz Mountains according to Observations made by
M. Eschenhagen in 1888 and 1890.
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80 G. R. PUTNAM [Vol. III. No. 2.J
the vertical force is in excess, the maximum being at Ilfeld, amount-
ing to .00398 C. G. S. units. On the principle used by Fritsche,
that immediately over a magnetic disturbance the horizontal force
will not be affected, and that the inclination will be normal at sta-
tions so located that the direction of the disturbing mass coincides
with the normal inclination, a computation was made of the prob-
able depth of the disturbing mass. Normal inclination was found
at Hesserode, and normal horizontal intensity near Benneckenstein.
The resulting depth is from 18 to 34 kilometers. One objection
in this method of reasoning is, that at such depths the heat would
be so great as to prevent strong permanent magnetization. On
the other hand, little is known of density at these depths, and,
moreover, magnetization through induction is greater at high tem-
peratures.
The geology of the Harz region has been extensively studied,
and the author gives a brief review of the probable geologic his-
tory of this region. The granite here found has more capacity for
magnetization than the other formations. It is believed that the
more strongly magnetic granite is the denser, and hence is found
deeper down. At the two stations where the greatest local mag-
netic disturbance was observed, it is thought that this more strongly
magnetic granite has approached the surface, causing local mag-
netic attraction. The distribution of the granite masses in the
Harz, and the probable direction taken beneath the surface, are
shown in Chart II.
The Prussian Geodetic Institute has determined the deflection
of the plumb line for a considerable number of points in the Harz,
which are shown on Chart I by the black circles, near each of
which the amount of the deflection in the meridian is given in seconds
of arc — positive fpr deflections toward the south, and negative to-
ward the north. * The greatest south deflections are found at Harz-
burg (12". 7) and Kattenase (i3".4), at the north edge of the Harz.
Passing south, the deflection rapidly diminishes, becoming zero
between Achtermannshohe and Andreasberg, and then becoming a
north deflection, which reaches its maximum at Tettenborn (6".i).
The line of no deflection is shown on Chart I, and is seen to be
nearly parallel to the magnetic ridge line. It is also considerably
south of the highest summits of the mountains, due, undoubtedly,
to the fact that these highest summits are nearer the northern edge
of the Harz, and possibly also to unequal distribution of densities
beneath. This displacement of the zero deflection line to the
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MAGNETIC ANOMALIES IN HARZ MOUNTAINS 8 1
Chart II.— Distribution cf the Granite Masses in the Harz Mountains.
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82 G. R. PUTNAM [Vou III, No. a.]
southward would accord with the indication given by the magnetic
ridge line of heavier granite masses still further to the southward.
It will be interesting to note whether such relations between mag*
netic disturbances and plumb line deflections are developed in other
regions. The author points out that the anomalies in the vertical
force alone would be sufficient for such comparisons, and he states
that it would not be difficult to obtain the necessary observations
for this purpose with a single instrument, of whose construction
the details are not given.
As early as 1887, Naumann sought to explain such magnetic
disturbances by supposing diversions of the earth currents in con-
sequence of disturbances of the strata of the mountains. In reply,
the author states that very little is known of earth currents, while
the permanent magnetic properties of some of the formations com-
posing mountain masses have been carefully investigated and are
well known.
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ERDMAGNETISCHE OBSERVATORIEN UND ELEC-
TRISCHE BAHNEN.
Von M. Eschknhagen in Potsdam.
Bei der grossen Ausbreitung, welche in neuester Zeit der Be-
trieb elektrischer Bahnen im Stadtverkehr, sowie auch zur Verbin-
dung mebrerer Orte unter einander gewinnt, scheint die Zeit nicht
mehr fern, dass die Beobachtungen der erdmagnetischen Erschein-
ungen durch jene Betriebe mindestens sehr beeintrachtigt, wenn
nicht ganz verhindert werden.
Zu Washington und Toronto (Canada) ist dies bereits der Fall 1 ,
wahrend in Deutschland eine ganze Reihe physikalischer Universi-
tats-Institute an der Ausfiihrung magnetometrischer Messungen
verhindert und die Beobachtungen an Galvanometern wesentlich
auf unempfindliche Instruinente beschrankt sind.
In den eingehenden Besprechungen, welche dieser Prage im
weitesten Sinne in zwei Sitzungen des " elektrotechnischen Vereins
zu Berlin" im Mai und Juni des Jahres 1895 zu Theil geworden
sind (vergl.Sitzungsberichte Heft 27 und 28 1895 der "Elektrotechn.
Zeitschrift"), ist von Gelehrten wie Technikern allgemein anerkannt
worden, dass die bei gewissen elektrischen Bahnen mit Riicklei-
tung durch die Erde auftretenden sogenannten vagabondirenden
Erdstrome das magnetische Feld in weitem Umkreise in einer ganz-
lich unkontrolirbaren Weise storen. Jene Strome, welche in den
oberen Schichten der Erdoberflache zwischen Punkten mit ver-
schiedener Spannung cirkuliren, erlangen eine verschiedene Aus-
breitung je nach dem augenblicklich herrschenden Feuchtigkeits-
zustande des Bodens, sowie nach Massgabe der Stromstarke und
Strotnrichtung, welche beide mit dem Betriebe ziemlich stark wech-
selnde Betrage erlangen. Von Herrn Ober-Ingenieur Strecker an-
gestellte Versuche (vergl. "Elektrotechn. Zeitschrift" 1896, Heft 7,
Seite 106) iiber die Ausbreitung der elektrischen Strome in die
Erde haben gezeigt, dass in einer 17 km. von der Bahnlinie ent-
fernten sekundaren an die Erde angeschlossenen Drahtleitung noch
Strome inducirt wurden, welche mit dem Telephon wahrnehmbar
waren.
1 Vergl. dxese Zeitschrift 1897, Heft IV.
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84 M. ESCHENHAGEN [vol. ni, No. 2.)
In den oben erwahnten Besprechungen des elektrotechnischen
Vereins ist denn auch von alien Seiten anerkannt worden, dass die
eigentlichen erdmagnetischen Beobachtungen in Zukunft nur in
einem hinreichenden Abstande von jenen elektrischen Bahnen
angestellt werden konnen, da es einen Schutz gegen die Modifika-
tion des Erdfeldes durch jene Strome nicht giebt und das Auftreten
derselben, so lange die Erde als Riickleitung benutzt wird, nicht
verhindert werden kann.
Durch Anwendung von Instrumenten nach dem Typus d'Arson-
val kann zwar bei vielen rein physikalischen Arbeiten der storende
Einfluss elektrischer Anlagen beseitigt werden, fur die erdmagneti-
schen Untersuchungen gilt dies jedoch nicht, da es sich hier eben
um die Erforschung des in keiner Weise kunstlich beeinflussten
erdmagnetischen Feldes handelt.
Es erwachst daher den magnetischen Observatorien die Auf-
gabe, sich dieser Storungen zu erwehren und diejenige Entfer-
nung festzustellen, bis zu welcher die Annaherung jener Bahnen
gestattet werden kann, eine Frage, die auch bei einer nothwendig
werdenden Verlegung der Observatorien entschieden werden muss.
Es ist wohl nothig, sich hierbei des Umstandes zu erinnern, dass
durch jene storenden Einfliisse die Mitarbeiterschaft vieler physi-
kalischer Institute unserer Universitaten an der Vervollkommnung
erdmagnetischer Instrumente und Messmethoden mehr oder minder
unmoglich gemacht wird. Es wird also nothig werden, in den
magnetischen Observatorien Platze zu reserviren, an denen die
allerfeinsten Untersuchungen an magnetischen Messinstrumenten
ungestort angestellt werden konnen und an denen der Erdmag-
netismus und die Erdstrome unbeeinflusst auch in den kleinsten
Veranderungen wahrgenommen werden konnen. Andernfalls wird
man es nicht mit den Beobachtungen einer Naturerscheinung,
sondern mit einem ktinstlichen, vollkommen unregelmassigen
Phanomen zu thun haben.
Von diesen Erwagungen ausgehend hat die Direktion des Ob-
servatoriums in Potsdam an die staatliche Aufsichtsbehorde das
Verlangen nach einem Schutzkreise von vorlaufig 15 km. Radius
gerichtet, innerhalb dessen Anlagen mit jener storenden Wirkung
nicht gestattet werden sollen. Diesem Ersuchen ist vorlaufig
entsprochen worden. Eine Beeintrachtigung des Verkehrs wird,
um dies vorweg zu sagen, voraussichtlich nicht oder nur voriiber-
gehend eintreten konnen, da der Betrieb von Wagen durch Accu-
mulatoren in einer wesentlich geringeren Entfernung kein Bedenken
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MAGNETISCHE STORUNGEN ELECTRISCHER BAHNEN 85
hat Ferner ist anzunehmen, dass es der fortschreitenden Technik
gelingen wird, das Auftreten der vagabondirenden Strome oder doch
ihre schadliche Wirkung durch andere Methoden der Strom-
erzeugung und Fortleitung, z. B. durch Benutzung von Wechsel-
strom, zu beseitigen.
Der Grund, eine so weitgehende Forderung zu stellen, beruht
auf der zunehmenden Empfindlichkeit der magnetischen Apparate,
die zu Untersuchungen der kleinsten Schwankungen des Erdmag-
netismus erforderlich ist. Denn man muss wohl den Grundsatz
festhalten, dass jede St'drung, die iiberhaupt zur Wahrnehmung
kommt, eine Beeintrachtigung der erdmagnetischen Forschung
bereitet. In Potsdam registrirte man noch Intensitatsschwankun-
gen an einem Instrument, das einen Skalenwerth von 1 mm. =
0.3 y = 0.000003 C. G. S. besass. Man erkennt noch gut 1/10 die-
ses Betrages, also 0.03 y, was einer Richtungsanderung von A$ =
A H
—— 7 = o'.oo55 = o".33 entsprechen wiirde. Es miissten also
H sin 1 ^ r
die Ablenkungen durch die Bahnstrome unterhalb dieses Betrages
bezw. des jener oben angegebenen Intensitatsanderung von 0.03 y
bleiben, wahrend sie sich jetzt in den betroffenen Observatorien
leicht bis zu 5' und 6', also dem tausendfachen erheben. Man darf
iiberdies wohl annehmen, dass bei eigentlichen Erdstrombeobach-
tungen gerade jene kleinen aber sehr schnellen Stromschwankungen
im Galvanometer noch viel starker wahrnehmbar sein werden.
Das Festhalten eines Schutzkreises von 15 km. Radius durfte
daher wohl unerlasslich sein, wenn man erwagt, dass bis zu diesem
Abstande noch die Ausbreitung der in der Erde cirkulirenden
Bahnstrome nachgewiesen ist. Auf Magnetometer wird dann vor-
aussichtlich keine Wirkung mehr zu konstatiren sein, aber die
Anstellung wvon eigentlichen Erdstrombeobachtungen wird ver-
muthlich doch noch beeintrachtigt, und es durfte in Zukunlt schwer
werden, fur dieselben iiberhaupt noch einwurfsfreie Beobachtungs-
linien in cultivirten Gegenden zu finden.
Fur die magnetischen Observatorien ist es nun zunachst das
Wichtigste, sich nicht durch die Anlage von elektrischen Bahnen
iiberraschen zu lassen, wie es den physikalischen Instituten ergan-
gen ist, sondern rechtzeitig Protest zu erheben. Andernfalls muss
es dahin kommen, dass die Kontinuitat der Beobachtungsreihe des
Observatoriums unterbrochen wird, womit dasselbe auch als Basis-
station fur die magnetische L,andesaufnahme unbrauchbar wird.
Damit ist aber eine sichere Konstruktion magnetischer Karten, die
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86 M. ESCHENHAGEN [vol. hi. No. *.]
fur Theorie and Praxis des Erdmagnetismus gleich wichtig sind,
in Frage gestellt.
Stellt sich aber die Verlegung eines Observatoriums als unum-
ganglich beraus, so ist hierfiir durch jenen Protest die nothige Zeit
gewonnen, um vorerst sichere Anscblussbeobacbtungen anzustellen
durch den Vergleich des alten und des neuen Platzes.
Es werden Seitens des Potsdamer Observatoriums in nachster
Zeit Versuche angestellt werden, uui den Einfluss der elektrischen
Bahnen in verschiedenen Entfernungen festzustellen, wenn mog-
lich durch photographische Registrirung. Auch soil untersucht
werden, ob etwa ein Schutz durch Wasserlaufe, Fliisse oder Seen
eintritt, wenn dieselben jene in der Erde cirkulirenden Strome in
sich aufnehmen. Die gesammelten Erfahrungen werden hier zur
Kenntnis gebracht werden. Inzwischen ware es sicker von Nutzen,
wenn auch andere Observatorien ihre etwa bcrcits gemachten Er-
fahrungen mitthcilcn wollten.
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LETTERS TO EDITOR
Photographic Reproductio: 3 op Plates in Lamont's Handbuch
des Erdmagnetismus (1849). — Professor Max Eschenhagen, in charge
of the Potsdam Magnetic Observatory, informs the editor that he is in a
position to be able to furnish those possessing a copy of Lamonts well-
known work, in which the plates are missing, with photographic repro-
ductions of the same at cost price.
Mean Magnetic Elements for the Year 1897 at Observatory
Infant D. Luiz (Lisbon). — The following data 1 have been courteously
sent the Journal by the director, Senhor Capello :
Declination Diurnal Variation Inclination Intensity in C. G. S. Units
(te__±*r*) f * _j£\ Horizontal Vertical Total
17° 3i r -55 W ^.23 58°o8 / .20 0.23385 0.36724 0.44299
"The values deduced from the five selected days in each month have
not yet been calculated." (Lisbon, Jan. 12, '98.)
United States Hydrographic Office Magnetic "Variation"
and Dip Chart for the Year 1900. — Mr. Littlehales writes: "Much
new information, relating to both declination and inclination, has been
received since the chart for the epoch 1897 was prepared, and the pres-
ent chart represents the improvements due to these later data " This
chart is on the same scale as those for 1897.*
International Conference on Terrestrial Magnetism and
Atmospheric Electricity. — Letters received from various eminent
magneticians give every indication that the meeting will be a successful
one. As it is the expectation of the editor to attend the Conference, the
next issue of the Journal will be unavoidably delayed.
1 For the values 1890-96, cf. Vol. II, p. 119.
*C/. Vol. II, p. 157.
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ABSTRACTS AND REVIEWS
MAGNETIC OBSERVATIONS IN SICILY IN 1890.
Palazzo, Luigi. Misure di Magnetistno Terrestre fatte in Sicilia nel i8go.
Roma, 1897. 1
In the year 1890 the director of the Central Office for Meteorology and
Geodynamics proposed to carry out a complete magnetic 9urvey for the whole
of the Island of Sicily. Much time had elapsed since Professor Chistoni's
survey of 1881, and it became desirable to extend his observations, and in
particular to elucidate more fully the distribution of the magnetic lines over
the vulcanic regions.
The work was assigned by Director Tachini to Professor Chistoni and
to the author, and it was to include also some station* in adjacent territo-
ries. Observations were made by Professor Chistoni at points in the interior,
as well as on the east and west coasts of Sicily ; also, on Mount Etna, These
observations were published in Vol. XI, Part 3, of the Annals. Stations to
the southwest of the island, and those in Malta and Tunis, were reserved for
the author, and for the purpose of connecting the survey with that under-
taken, on the part of France, by Moureaux in this part of the Mediterranean.
The stations occupied were : Palermo (a place in common with Chistoni's
measures for comparison of instruments), Ustica, Tunisi, Pantelleria, Trapani,
Mazzara del Vallo, Sciacca, Lampedusa, Linosa, Girgenti, Licata, Vittoria,
Cozzo Spadaro, Malta, and Roma. The results at the Sicilian stations, up to
the close of the year 1892, were presented by Professor Tachini to the Italian
Geographical Congress at Genoa. They are now given revised and in greater
detail. The same instruments were used as in 1888-89, except as to a small
magnetometer specially constructed for the investigation of the disturbed
regions of the vulcanic rocks. The instrumental constants are investigated
at length. The complete record and the results for each station follow next
At Palermo, the results by the two observers are in fair accord ; viz., differ-
ence in declination, +i'.$: in dip, -\-i'.t: and in horizontal component,
—0.00012 (C. G. S.) On the other hand, at Tunisi, the differences between
the Italian and French observers are somewhat greater ; viz., +4'-5» +3 / «7»
and — 0.00099 respectively. But these figures depend on the mean of two or
three stations. As the result of the instrumental differences at Tunisi and
Malta, we have -f-6',2, -f i'.8, and —0.00088 respectively. The series closes
with the record and results of observations made at Rome in June, 1890, on
the occasion of the visit of two Austrian observers engaged upon the mag-
netic work of the Adriatic. The last page of the memoir contains a recapit-
ulation of the results. C. A. S.
1 Annali delV Ufficio Centrale Meteorologico e Geodinamico. Vol. xviii, parte 1.
1896.
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MAGNETIC OBSERVATIONS 89
MAGNETIC OBSERVATIONS IN MEXICO.
Moreno y Anda, Manuel. — E studio Sobre el Magnetismo Terrestre en Mix-
ico. Mexico, 1895.
Observations Magnttiques faites a V Observatoire
Astronomique National de Tacubaya, pendant Pannee 1895. Sociedad
Cientifica "Antonio Alzate ," Mexico, 1896.
In the exordium of the address given in the first paper, and presented
before the principal scientific society of Mexico, the author holds up before
the people of the Republic a collection of magnetic observations relating to
places on their soil, taken from the papers on Terrestrial Magnetism in the
late reports of the United States Coast and Geodetic Survey. Taking some
of the most complete collections of observations at such places as Vera Cruz,
Acapulco, and San Bias, he portrays the difficulties that beset the investigator
who attempts to deduce the course of the needle from them, setting forth their
utter lack of concordance because they have not been taken with the same
instruments or with instruments that have been compared with one another
or with the same standard instrument ; because they have not been related to
the same part of the daily, monthly, yearly, or decennial cycles of the mag-
netic needle; because, of those compared, some may be abnormal on account of
the prevalence of magnetic storms when they were taken ; and because, more-
over, the different observations making up a series were in no case made
upon the same spot iu the same locality. Then, telling his audience that those
observations and those investigations represent, in the present state of our
knowledge, the best that can be known of the geomagnetism of Mexico and
the secular course of the magnetic needle there, and pointing out the unique
position and scientific value of the Mexican Observatory on account of its al-
titude, its geographical latitude, and its relation to other magnetic observa-
tories, he appeals for a continuation of the series of observations that are
now being carried on at Tacubaya under his charge, and the protection of the
Observatory in its isolation from artificial electric and magnetic disturbances,
in order that future generations, profiting by the material that will be be-
queathed to them by ours, may be led to the solution of problems that
baffle us.
The instrumental equipment of the Magnetic Department of the Na-
tional Astronomical Observatory at Tacubaya consists of an uni filar mag-
netometer by Elliott and a dip-circle by Dover. The author describes the
mounting of these intruments and their surroundings at the observatory,
states the constants of the magnetometer which were determined by the offi-
cials of the Magnetic Observatory at Kew before the instrument was exported
from England, and describes the methods of observation and calculation of
the results, which are those ordinarily used. The results of the magnetic dec-
lination, inclination, and intensity, observed in December, 1893, and January,
February, April, and May, 1894, which form a part of this paper, are stated in
connection with the summary of Mexican magnetic observations which
follows :
In the report given in the second paper the author states that the opera-
tion of the Mexican Magnetic Observatory has proceeded without interrup-
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90
ABSTRACTS AND REVIEWS
[Vol. Ill, No. 2.J
tion since the date of the observations which were printed in his first paper ;
and that no modification has been made in the equipment, nor any change in
the methods of observation and calculation. The report is taken up with
the details of the results of which the following is a summary, in which is in-
cluded those mentioned as being published in the author's work of 1895, and
also those of 1896, which were communicated by him in manuscript:
DECLINATION
INCLINATION
INTENSITY IN C. O. 8. UNITS
1879
1893
I894
1895
I896
Dec.
Dec.
Jan.
Feb.
April
May
Sept
Oct
Nov.
Dec.
Jan.
Feb.
Mar.
April
May
June
July
Aug.
Sept
Oct
Nov.
Dec.
Jan.
Feb.
Mar.
April
May
8° 21' 20"
41
10
42
44
42
47
42
40
43
16
46
15
42
27
45
49
43
03
44
07
40
43
41
38
44
31
45
55
46 32
45 4i
45 39
52 21
48 50
46 53
45 32
21
37
25 30
19 35
35 40
13 24
17 30
21 15
HORIZONTAL
44° 53' 26"
16 14
16 33
24 47
15
9
0.344I5
-3347
•3350
•3350
•3347
3345
.3342
•3343
3346
3339
•3343
•3344
3349
33365
.33368
33329
33266
33328
VERTICAL! TOTAL
O.3263
.3266
.3282
.3261
.3248
.3276
.3293
.3268
3299
.3253
3271
3275
.32654
.32652
32564
.32488
.32467
0.4675
4678
4690
4673
.4662
.468O
4692
4678
.4694
.4665
.4678
.4685
46686
.46693
.46597
.46458
.46528
The author has also kindly forwarded to the Journal, under date of
February 26, 1898, a brief account of the magnetic observations made at
Aguascalientes, Mexico, during the visit of the Mexican Commission ap-
pointed to observe the annular eclipse of the sun on the 29th of July, 1897.
The observations for declination and intensity were made with a portable
magnetometer set up in the orchard of the Institute of Sciences toward the
end of a northward-trending pathway, at a distance of five meters from the
adobe wall that bounds the orchard and ninety meters from the sign traced
on a brick wall. The observations for inclination were made with a dip-
circle situated seven meters from the magnetometer and two meters from the
adobe wall. The results given are the means of two needles. The mean
values of the observations made daily, at hourly or half-hourly intervals*
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MAGNETIC OBSERVATIONS
91
between 5 A. M. and 12 midnight of the local mean time of Aguascalientes,
are here summarized:
DATE
DECLINATION INCLINATION
INTENSITY IN C. O. S. UNITS
1897.
JULY
i
1 EAST NORTH
1 1
HORIZONTAL VERTICAL
TOTAL
24
25
26
27
28
29
30
; 1 47° W St"
1
| | 47 11 25
8° 15' 05" ,' 47 25 49
8 16 14 1 47 19 02
| 8 13 57 1
8 12 41 1 47 19 00
1
O.3248
O.323O
0.323I
0.3231
'. * '6666
0.48I3
0.4775
O.4766
O.4767
U. 5. Hydrographic Office.
G. W. Lit
T&EHALE
MAGNETIC ANOMALIES NORTH OF CHRISTIANIA. 1
In 1895 the author's attention was called to a somewhat anomalous mag-
netic declination on Mt. Kikud, N. of CHristiania, where, "as far as he could
judge by means of a map and an entirely reliable pocket-compass, it seemed
to be a trifle E., while at Christiania it amounted to 12 W." Several days,
during the summer of 1896, were devoted to more accurate observations on
Mt Kikud and other points in the province of Nordmark.
The instrument selected as best adapted for this purpose was the old Ertel
Diopter compass, formerly used by Hansteen in Siberia. The author shows
that the accuracy obtained by means of that compass is entirely satisfactory.
Friction between the agate cap and steel point supporting the needle — iti it-
self a small quantity, and perhaps further reducible by careful grinding —
proved to be the most important source of error to be avoided.
It happened that on the first day the author had to shift his stand about
teu yards, during a set of observations, on account of the position of the
sun (trees interfering). Between the two places thus consecutively occupied,
the difference in declination was found to be 6°, and so confirmed on the fol-
lowing day. This considerable anomaly, it seems, can only be"due to mag-
netic ore not far below the surface, although smaller local anomalies, to which
no immediate cause can be assigned, are frequent in the Nordmark, where the
rock is mostly syenitic and porphyric. None of the other stations observed
showed more than 2°.2 difference in declination from Christiania. (The pur-
pose of this publication of partly incomplete observations is mainly to point
out that even where the surface does not lead to any immediate suspicion
of underlying magnetic rock, considerable anomalies from this cause may be
looked for.)
An appendix contains a graphic representation of the declination and
horizontal intensity observations during the solar eclipse, August 9, 1896,
taken every five minutes, beginning four days before and ending one day
after the eclipse. Paui, Wernicke.
»Geelmuyden, H. : Nogle Magnetiske Observationer i Nordmarken og i
Christiania. Christiania, 1897. 19x22 cm. Pp.19. PI. 1.
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9 2 ABSTRACTS AND REVIEWS [vol. in, No. .]
THE MAGNETIC OBSERVATIONS OF THE BATAVIA MAGNETIC
OBSERVATORY.
Van der Stok.— Observations made at the Magnetic a I and Meteorological
Observatory at Batavia. Government Printing-office of Netherlands
India, Batavia, Vols. XVI, XVII, XVIII, XIX, 1893-4-5-6.
These large volumes (over 200 pages each, 26 by 36 cm.) are made up of
tables showing the results of observation and of certain computations. The
only text in each volume is a preface of one page only.
The magnetical portion of each volume gives the declination, horizontal
force, and vertical force for each hour during the year (36 pp.) ; gives the
" deviation " of each of these hourly values from normal conditions (36 pp.) ;
a summary of the monthly mean values of declination, horizontal, vertical,
and total intensity, and dip ; seven pages of tables exhibiting the solar di-
urnal variations in various aspects ; two pages showing the " mean hourly
and monthly amount of deviations ;" and one page showing the values and
numbers of the " disturbances " to each element
Vol. XVI, 1893, gives a summary covering the period 1882-93 inclusive.
The series is continuous from January, 1884. Twelve months are missing
during 1882-3. This general summary consists of a recapitulation of monthly
and annual values for each element (2 pp.) ; twenty-seven pages showing the
solar diurnal variations under various conditions; three pages are devoted to
the statistics of " deviations,* ' and six to the statistics of " disturbances," —
each "deviation" exceeding a stated limit being classed as a "disturbance."
The volume for 1894 contains twenty-nine pages of tables (without com-
ment or explanation) showing the lunar diurnal variation of the magnetic
elements. This variation is much larger when computed from "disturb-
ances" only, than when computed from all the observed values.
It is noted in Vol. XVIII that certain absolute measurements made at the
Observatory by officers of the French navy gave results for declination and
inclination agreeing well with those of the Observatory, but that the French
value for the horizontal force was 0.004 c « g- 8 « units greater than the Ob-
servatory value. This unexplained discrepancy serves again to indicate the
necessity of an intercompurison of the magnetic instruments at different ob-
servatories which are assumed to furnish absolute results.
While writing this review, Vol. XIX, giving the observations and results
for 1896, has been received. The arrangement is the same as in the previous
volumes, with the exception of certain improvements in headings and num-
bering of tables.
A few pages of explanation and comment inserted in each volume would
be valuable to the reader, and give him, doubtless, a better appreciation of
the important work that is being done at this observatory. For example, a
few lines would probably suffice to show how the " deviations " were com-
puted ; but in the absence of such explanation, a reader who has not access
to Professor van der Stok's previous papers is apt to lose much time if he
tries to make this discovery. John F. Hayford.
U. S. Coast and Geodetic Survey.
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THE NEW YORK
u, , r , at a HJBUC LIBRARY
Volume III Numbt r j
Terrestrial Magnetism, September, 189K
Alton, UNOX AND '
TILOEM FOUNDATION . I
THE INTERNATIONAL CONFERENCE ON TERRES-
TRIAL MAGNETISM AND ATMOSPHERIC
ELECTRICITY.
[Held in affiliation with Section A of the British Association, at Bristol,
September 7-14, 1898.]
It is with great pleasure that we announce that the Conference
was a success, and was attended by a majority of the members of
the Permanent International Committee. In the absence of the
representatives of the United States, Mr. C. A. Schott was co-opted
a member of the Committee.
Members of the Committee present : Messrs. Rucker, Eschen-
hagen, Liznar, Mascart, Moureaux, Palazzo, Rykatchew, Schmidt
(Gotha), Schott, and Schuster. Members of the Committee absent:
von Bezold, Bauer, Capello, Carlheim-Gyllenskold, Mendenhall,
and Paulsen. Others in attendance: Captain Creak, Professors
W. Grylls Adams, C. Vernon Boys, G. Carey Foster (London), Mr.
Kitto (Falmouth Observatory), Dr. Selim Lemstrom (Norway),
Sir Norman Lockyer (London), Professor Mathias (Toulouse), Dr.
Privat (Toulouse), Dr. Snellen (Utrecht), Professor Tanakadate
(Tokio), Professor H. H. Turner (Oxford), and others.
Dr. C. H. Lees, of the Owens College, Manchester, and one of
the secretaries of the Section of Mathematics and Physics, acted as
secretary to the Conference. Meetings of the Conference were
held on September 8th, 9th, 12th, and 13th, and of the Committee
on September 7th, 9th, 12th, and 13th.
In his address of Thursday, September 8th, the president of
Section A, Professor W. E. Ayrton, in welcoming those attending
the International Magnetic Conference, referred in an interesting
and striking manner to a matter of supreme importance to so many
of our magnetic observatories — that of disturbances from electric
tramways. Professor Ayrton's remarks on this subject will be
found in another place.
The proceedings of the Conference were opened by an address
from the president.
[See Professor Riicker's address. In this a full account is given of the
circumstances under which the Conference assembled.]
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94 PROCEEDINGS [vol. in, No. 3]
The business of the Conference was to consider four questions
(those marked by an asterisk below) 1 , referred to the Permanent
Committee by the International Meteorological Conference, and to
discuss such other questions as might be brought before them.
The proceedings were as follows :
Thursday, September 8th.
1. Address by the President.
2* Report on the relative advantages of long and short mag-
nets. Professor E. Mascart.
[See Professor Mascart's report]
3. On the construction of magnets of constant intensity under
changes of temperature. /. R. Ashworth.
[This paper was a resume* of a communication recently published
in the Proceedings of the Royal Society and in Terrestrial Mag-
netism, Vol. II, No. 4. Mr. Ashworth has found that some magnets
made of pianoforte wire have negative temperature co-efficients, and
that, under circumstances, detailed in his paper, it is possible to con -
struct magnets, the moments of which are independent of the tem-
perature.]
Friday, September 9th.
1* On the establishment of temporary magnetic observatories in
certain localities, especially in tropical countries. Professor
W. von Bezold and General Rykatschew.
[Given in full later on.]
2. Antrag auf Massnahmen zur systematischen Erforschung der
Saecular-Variationen der erdmagnetischen Elemente. Dr.
Adolf Schmidt {Got ha).
[Given in full elsewhere.]
3. Magnetische Simultan-Beobachtungen. Professor M. Eschen-
hagen.
[Professor Eschenhagen spoke of the importance of observing small
disturbances which he has detected* and made some. preliminary state-
ments as to the relative frequency of the occurrence of these disturb-
ances at different periods of the year.]
4* Discussion as to whether in calculating monthly means all days
are to be taken into consideration.
5* Discussion as to the publication of the differences between the
hourly and monthly means of the components of the mag-
netic forces.
l See Terrestrial Magnetism, Vol. Ill, page 68.
*See Terrestrial Magnetism, Vol. II, p. 105.
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INTERNATIONAL MAGNETIC CONFERENCE 95
6* On magnetic observatories in the Azores. Albert, Prince of
Monaco.
[Given in full elsewhere.]
7. On magnetic observations in Cape Colony. Dr. Beattie and Mr.
Morrison.
[Mr. Morrison announced that he and Dr. Beattie had begun a mag-
netic survey of the Colony.]
8. Sur le mouvement diurne du pdle nord d'un barreau magn£tique
suspendu par le centre de gravite\ J. B. Capello.
[Given in full elsewhere.]
Monday, September 12th.
1 . An account of the late Professor John Couch Adams's determi-
nation of the Gaussian magnetic constants. Professor IV.
Grylls Adams.
[A short account of the work done by the author's brother on the
theory of terrestrial magnetism, and of his determination of the
Gaussian constants. This work was first taken up by the late Pro-
fessor John Couch Adams, just fifty years ago, not long after the dis-
covery of the planet Neptune. The paper will be printed in full in
the Report of the British Association]
2. On a simple method ot obtaining the expression of the mag-
netic potential of the Earth in a series of spherical harmonics.
Arthur Schuster.
[Given in full elsewhere.]
3. On magnetic observations in Funafuti. Captain E. Creak.
[Captain Creak, superintendent of the Compass Department in the
British Admiralty, stated that during the recent expeditions to Fun-
afuti for the purpose of boring through the coral to the underlying
rock, magnetic observations were made on the island on a raft in the
lagoon and (for declination) at sea, in the neighborhood of the island.
A well-marked ridge line was discovered and two maxima of vertical
force disturbance, one of which was stated by Professor Riicker, in
course of the discussiou following Captain Creak's remarks, to be
more intense than any that had been discovered in the United King-
dom, except on, or close to basalt. Captain Creak claimed that the
magnet had thus been affected by rocks which had not been reached
by boring to a depth of nearly 700 feet.]
4. On the relations between the variations in the earth currents,
the electric currents from the atmosphere, and the magnetic
perturbations. Selim Lemstront.
[Given in full elsewhere.]
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96 PROCEEDINGS [vol. hi, no. 3]
5. On the interpretation of earth current observations. Arthur
Schuster.
[Given in full elsewhere.]
6. Some remarks on the construction of magnetic observatories.
Dr. M. Snellen.
[Being an account of the new magnetic observatory recently erected
near Utrecht. The paper has been promised for a future number of
1 errestrial Magnetism^
Tuesday, September 13th.
1. Joint discussion between members of Section A (Mathematics
and Physics), G (Mechanics and Engineering), and of the
International Magnetic Conference on " The Magnetic and
Electrolytic Actions of Electric Railways."
[The subject was opened by Mr. C. A. Schott, who was followed by
Messrs Riicker, Eschenhagen, Preece, Palazzo, Fleming, and others.
Abstract of discussion given elsewhere.]
After the discussion on electric railways the members of the
Conference adjourned to their own room, and the following papers
were read :
2. Sur Failure des lignes isomagnetiques aux environs du vulcan
^Bthna. Luigi Palazzo.
3. On the influence of altitude above the sea on the elements of
terrestrial magnetism. Drs. van Ryckevorsel and van Bern-
me ten.
4. Ueber die Aenderung der erdmagnetischen Kraft mit der Hohe.
Professor J. Liznar.
The Conference then adjourned.
During the session of the Permanent Committee an important
report to the International Meteorological Conference was agreed
to, and the president was authorized to publish it as soon as it
had been communicated to the secretary of that Conference.
EXTRACT FROM MR. SCHOTT'S REPORT ON THE CONFERENCE.
[As the Journal is passing through the press, a manuscript copy of the Report
on the Conference, made by Mr. Schott to the superintendent of the Coast and Ge-
odetic Survey, Dr. Henry S. Pritchett, has been received through Dr. Pritchett'9
courtesy. In closing his Report, Mr. Schott says :
"It is conceded by those who took an active part in the deliberations that this,
the first International Magnetic Conference, has been most satisfactory in its results,
and it is to be hoped that its fruits will show that the labor spent at Bristol was well
directed. Too much praise can not be bestowed upon the effective manner in which
the sessions of the Conference were presided over, which in no small degree contrib-
uted to the success of the meeting ; nor will the members ever forget the cordiality
of reception and generous hospitality extended to them by their president, the Brit-
ish Association, and the Chamber of Commerce of the city of Bristol."— Ed.]
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INTERNATIONAL MAGNETIC CONFERENCE.— WELCOM-
ING ADDRESS. 1
By Professor W. E. Ayrton, F. R. S.
Section A this year is very fortunate in having its meetings as-
sociated with those of an " International Conference on Terrestrial
Magnetism and Atmospheric Electricity/ ' which is attended by the
members of the " Permanent Committee for Terrestrial Magnetism
and Atmospheric Electricity " of the "International Meteorolog-
ical Conference." It has been arranged that this Permanent Com-
mittee, of which Professor Rucker is the president, shall form
part of the General Committee of Section A, and shall also act as
the Committee of the International Conference, which will itself
constitute a separate department of Section A. For the purpose,
however, of preparing a Report to the International Meteorolog-
ical Conference, and for similar business, this Permanent Commit-
tee will act independently of the British Association.
My first duty to-day, therefore, consists in expressing the
honor and the very great pleasure which I feel in bidding you,
members of the International Conference, most heartily welcome.
Among the various subjects which it is probable that the Con-
ference may desire to discuss, there is one to which I will briefly
refer, as I am able to do so in a triple capacity. The Earth is an
object of much importance, alike to the terrestrial magnetician, the
telegraph electrician, and the tramway engineer; but while the first
aims at observing its magnetism, and the second rejoices in the ab-
sence of the Earth currents which interfere with the sending of
messages, the third seems bent on converting our maps of lines of
force into maps of lines of tramway.
It might, therefore, seem as if electric traction— undoubtedly a
great boon to the people, and one that has already effected impor-
tant social developments in America and on the continent of Eu-
rope — were destined in time to annihilate magnetic observatories
near towns, and even to seriously interfere with existing telegraph
and telephone systems. Already the principle of the survival of
» Extract from Opening Address by Professor W. E. Ayrton, F. R. S., the Presi-
dent of Section A (Mathematics and Physics) of the British Association, at the
meeting, at Bristol, England, September 7-14, i8$8.— Nature, Vol. I*VIII, No. 1506,
September 8, 1898, pp. 448, 449.
97
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98 W. E. AYRTOX [vol. hi, No. 3 .]
the fittest is quoted by some electrical engineers, who declare that
if magnetic observatories are crippled through the introduction of
electric tramways, then so much the worse for the observatories.
And I fear that my professional brethren only look at me askance
for allowing my devotion to the practical applications of electricity
to be tainted with a keen interest in that excessively small, but
none the less extremely wonderful, magnetic force which controls
our compass needles.
But this interest emboldens me to ask again, Can the system of
electric traction that has already destroyed the two most important
magnetic observatories in the United States and British North
America be the best and the fittest to survive? Again, do we take
such care, and spend such vast sums, in tending the weak and nurs-
ing the sick because we are convinced that they are the fittest to
survive? May it not perhaps be because we have an inherent
doubt about the justness of the survival of the strongest, or be-
cause even the strongest of us feels compelled to modestly confess
his inability to pick out the fittest, that modern civilization en-
courages, not the destruction, but the preservation of what has ob-
vious weakness, oa the chance that it may have unseen strength?
When the electrical engineer feels himself full of pride at the great-
ness, the importance, and the power of his industry, and when he is
inclined to thiuk slightingly of the deflection of a little magnet com-
pared with the whirl of his i ,000-horse power dynamo, let him go
and visit a certain dark store-room near the entrance hall of the
Royal- Institution, and, while he looks at some little coils there,
ponder on the blaze of light that has been shed over the whole
world from the dimly-lighted cupboard in which those dusty coils
now lie. Then he may realize that while the Earth as a magnet
has endured for all time, the earth as a tramway conductor may at
no distant date be relegated to the class of temporary makeshifts,
and that the raids of the feudal baron into the agricultural fields of
his neighbors were not more barbarous than the alarms and ex-
cursions of the tramway engineer into the magnetic fields of his
friends.
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INTERNATIONAL MAGNETIC CONFERENCE.— OPENING
ADDRESS.
Bv Prof. A. W. Rucker, M. A., D. Sc., Sec. R. S., President of the
Conference.
The President of the Section of Mathematics and Physics has
already expressed the pleasure with which British physicists wel-
come the distinguished band of visitors who have assembled to
take part in the International Conference on Terrestrial Magnet-
ism. None join in that welcome with more cordiality than those who
are especially interested in the science with which the Conference
will be occupied. To us it is a source both of gratification and
pride that the International Committee, to whose action this meet-
ing is due, should have allowed us to play the part of hosts to the
eminent men from many lands who have responded to their call.
Some, whom we would gladly have seen here, but who have been
prevented from attending by various causes, have nevertheless
shown the interest which they take in our proceedings by sending
written communications. Thus our meeting is as fully representa-
tive as we could have hoped.
It may be interesting to those who are unaware of the fact if I
remind the Conference that this is not the first occasion on which
students of terrestrial magnetism have taken counsel together dur-
ing a meeting of the British Association.
Fifty-four years ago the then President of the Association, the
Very Rev. George Peacock, Dean of Ely, stated in his address that
the period was drawing to an end for which a series of magnetic
observatories had been established by international co-operation.
44 Six observatories,' ' he stated (Brit. Assoc. Rep., 1844, p. xliv),
" were established, under the zealous direction of M. Kupffer, in
different parts of the vast empire of Russia, the only country, let
me add, which has established a permanent physical observatory.
The American Government instituted three others, at Boston, Phil-
adelphia, and Washington ; two were established by the East India
Company at Simla and Singapore; from every part of Europe, and
even from Algiers, offers of co-operation were made." The ob-
servatories thus provided for were to be carried out for three years
only; but as nearly the whole of that time was spent in prepara-
tion, the period was doubled. When the term thus fixed drew to
99
200379
IOO A. W. RUCKER. [Vol. Ill, No. 3.)
an end, the question arose as to whether it was desirable to extend
it further, and M. Kupffer (Director-General of the Russian Sys-
tem of Magnetic and Meteorological Observations) addressed a let-
ter to Colonel (afterwards Sir Edward) Sabine, suggesting the pro-
priety of summoning a Magnetic Congress to be held at the next
meeting of the British Association.
In accordance with that suggestion the Congress was held dur-
ing the meeting of the Association at Cambridge in 1845. The
number of distinguished foreigners who attended in person was
considerable in spite of the difficulties of travel fifty years ago.
Amongst those who were present were M. Kupffer; Dr. Erman, of
Berlin, the celebrated circumnavigator and meteorologist; Baron
von Senftenberg, the founder of the Astronomical and Meteorolog-
ical Observatory of Senftenberg in Bohemia ; M. Kreil, the direc-
tor of the Imperial Observatory at Prague ; Dr. von Boguslawski,
the director of the Royal Prussian Observatory at Breslau ; Herr
Dove, professor of physics in the University of Berlin ; and Baron
von Waltershausen, a gentleman who had taken part in the mag-
netic observations of Gauss and Weber at Gottingen, and had exe-
cuted a magnetic survey of portions of Italy and Sicily. In addi-
tion to these a number of well-known British men of science were
invited to be present, amongst whom I need only mention the
Marquis of Northampton (President of the Royal Society), Sabine,
Sir John Herschel, Lloyd, Airy, Brown, and Sir James Ross, then
recently returned from his celebrated expedition to the Antarctic
seas. Letters were also received from Wilhelm Weber, Gauss,
Loomis, Lamont, Quetelet, Von Humboldt, and others.
The principal question which this Conference had to decide was
whether " the combined system of British and foreign co-operation
for the investigation of magnetic and meteorological phenomena,
which [had then] been five years in progress, must be broken up "
(Brit. Assoc. Rep., 1845, p. 69). I will not trouble you with a re-
capitulation of the recommendations of the Congress, some of
which have been carried out, while others have not yet been real-
ized ; but one resolution will, I am sure, so exactly express your
own sentiments, that I venture to quote it, viz. : " That the cordial
co-operation which has hitherto prevailed between the British and
foreign magnetic and meteorological observatories having produced
the most important results, and, being considered by us as abso-
lutely essential to the success of the great system of combined ob-
servation which has been undertaken, it is earnestly recommended
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INTERNATIONAL MAGNETIC CONFERENCE IO i
that the same spirit of co-operation should continue to prevail."
Whatever changes half a century may have wrought in the prob-
lems which press upon magneticians, and in the difficulties which
confront them, there can be no doubt that they are still of the same
spirit as that in which this resolution was framed.
It is true that we sometimes meet with the objection that interna-
tional conferences of all kinds are now too numerous, and that their
decisions, from their very number and complexity, cease to attract
attention or to command respect. Admitting that this objection is
not without weight, it may be answered by two remarks. The
closer union between scientific workers in different countries which
these meetings encourage, the strengthening of the ties of intellect-
ual sympathy by those of personal friendship, are in themselves
good. It is surely a hopeful omen that science, as she reaches her
maturity, forgets or ignores the political and geographical bounda-
ries which sometimes seemed so important in her youth, and that
workers for the common good are more and more learning that it
is good to work in common.
But there are special and cogent reasons why the science of
Terrestrial Magnetism should be cosmopolitan. The advance of
some sciences is most easily achieved by the methods of guerrilla
warfare. In a hundred different laboratories, widely separated
workers plan independent attacks on nature. In different univer-
sities and colleges little groups are devising stratagems and arrang-
ing ambuscades in the hope of wresting from our great opponent
some of the treasures which she yields only to the violent who
take them by force. But for those who would unravel the causes
of the mysterious movements of the compass needle, concerted ac-
tion is essential. They can not, indeed, dispense with individual
initiative, or with the leadership of genius ; but I think that all
would agree that there is urgent need for more perfect organiza-
tion, for an authority which can decide, not only what to do, but
what to leave undone.
The advance of the science of Terrestrial Magnetism must de-
pend upon the establishment, the maintenance, and the utiliza-
tion of the records of observatories. The bulk of the material to
be dealt with must in any case be vast, and every needless addition
to it, every obstacle in the way of its being readily comprehended
and easily used, is a drawback which proper organization should
prevent.
Thus it is wasteful to devote to the multiplication of observa-
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102 A. W. RUCKER [vol. in, No. 3)
tories, in regions of which we know much, energy and funds which
would be invaluable if applied to districts of which we know little
or nothing. I take some credit to myself in that, within the last
few months, I have assisted in checking well-intended but mistaken
proposals to add to the number of the magnetic observatories which
we already possess in this country.
Again, it is desirable that the records of the observations should
be so published as to be ready for application to the problems the
solution of which they are intended to subserve, and that the indi-
vidual worker should not be harassed by petty differences in the
methods of presentment, which often entail on him labor too enor-
mous to be faced. On this point something has already been done
by international co-operation, and we may hope that this meeting
will do much to complete the task.
Lastly, there are many investigations which are now undertaken
independently at irregular intervals which would be far more use-
ful if planned in common. Thus there has of late been a great
outburst of energy in Europe devoted to magnetic surveys more
detailed than have ever before been accomplished. Is it too much
to hope that, when the time comes for these to be repeated, they may
be carried out simultaneously, and reduced by the same methods,
so that we may have a magnetic map of Europe in which no un-
certainty as to the accuracy of details is introduced by the neces-
sity for correcting for the secular change over long intervals of
time?
Taking it for granted, then, that international co-operation is
desirable for purposes such as these, I come next to the question of
the nature of the machinery by which it shall be secured. And
here I may at once state that the arrangements under which we are
meeting to-day are in some respects abnormal, and that plans for
the future will have to be formally or informally considered before
we part. Meanwhile, it is desirable that I should state precisely
the circumstances which have brought us together.
The last meeting of the International Meteorological Confer-
ence was held in Paris in September, 1896. It was attended by
several men of science specially interested in Terrestrial Magnet-
ism, and, perhaps on this account, a new departure was taken by
the International Committee in the appointment of a " Permanent
Committee for Magnetism and Atmospheric Electricity," to which
certain specific questions were referred. Eight gentlemen were
nominated as members of this Committee, with power to add to
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INTERNATIONAL MAGNETIC CONFERENCE 103
their number. We in turn co-opted eight other magneticians, tak-
ing care that as far as possible all countries in which Terrestrial
Magnetism is specially studied should be represented. About the
same time, and, as I believe, iu ignorance of the establishment of
this Committee, a suggestion for the assembling of an International
Conference on Terrestrial Magnetism was made in the Journal of
that name by Professor Arthur Schuster. It appeared to me, and
to Professor Schuster himself, that it would be a great pity if this
suggestion resulted in the establishment of a rival organization,
and I at once submitted to the Committee the question whether, in
their opinion, it was desirable that we ourselves should take the re-
sponsibility of summoning an International meeting, with the view
of obtaining a wide discussion of the points submitted to us by
the Meteorological Conference. This suggestion was approved,
and as the British Association was willing to allow us to organize
the Conference as a branch of Section A (Mathematics and Phys-
ics), to undertake the expense of sending out the necessary notices,
to print our papers in its Report, and to extend to foreign members
of the Conference all the privileges of foreign members of the As-
sociation, it was also determined that so hospitable an invitation
should be accepted with the gratitude it deserved. But although
the main result has been achieved, and a representative gathering
of magneticians has assembled in Bristol, it can not be denied that
our relations to the various bodies with which we are connected
are somewhat complicated, and that our constitution is devoid both
of simplicity aud symmetry. I take it that these facts are signs of
health and vigor rather than symptoms of decay. Terrestrial Mag-
netism has beeu attracting far more attention of late years than in
the not very distant past. The necessity for meeting for common
action, for common publication, has been forced upon us. We
have cared more for meeting than for the terms on which we were
to meet, more for acting together than for drawing up an elaborate
deed of partnership, more for the promotion of science than for a
flawless paper constitution. Thus, and in my opinion most wisely,
we have sought to attain our ends, not by starting a brand-new
International Association, but by making use of machinery which
is already in existence, which has stood the test of time, and is, as
I believe, capable of being put to new uses in meeting our wants
and supplying our deficiencies.
I confess, however, that in this arrangement we have been com-
pelled to pay scant attention to the simplicity, and even to the log-
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104 A. W, RUCKER, [vol. hi, no. 3 .1
ical consistency, of our schemes. We are an International Confer-
ence on special subjects — Terrestrial Magnetism and Atmospheric
Electricity — summoned by a Committee owing its authority and
bound to report to another International Conference of wider
scope, which regards our sciences as branches of Meteorology.
On the other hand, this Committee is for the moment a part of
the Committee of the Section of Mathematics and Physics of the
British Association, though it retains its right of separate meeting,
more especially for the discussion of its report to the International
Meteorological Conference. It is evident that here there is plenty
of opportunity for collision between rival authorities, for confusion
between conflicting jurisdictions ; but to all questions as to the pre-
cise limits of authority and jurisdiction it is sufficient to reply in
the most general terms. The whole of the arrangements are tem-
porary, to meet an immediate pressing need. The work of the Con-
ference will be conducted like that of a Department of the British
Association. The members of the International Committee will
act as the Committee of the Department, but some of their work
will be done on the General Committee of Section A, of which
other magneticians will also be members. Should it be necessary,
they will hold some separate meetings, and some such meetings will
certainly be necessary to discuss their report to the Interna-
tional Meteorological Conference. These general regulations will
probably suffice for all practical purposes. If cases occur which
they do not cover, we must deal with them as they arise.
With regard to the future, I do not propose to lay before you
any detailed scheme, but in discussing the matter among ourselves,
the following principles should, in my opinion, be adhered to. The
International Meteorological Conference has held a number of suc-
cessful meetings. I believe that I am correct in saying that the
right to attend that Conference was at first confined to those who
were officially connected with Meteorological and Magnetic observ-
atories, but that of late invitations have been more widely dis-
tributed. If the authorities of that Conference see their way to
inviting in future most or all of those who are known to be specially
interested in Terrestrial Magnetism, I do not see why the Magnetic
Conference, which would then be constituted once in five years,
should not meet all our requirements. If, however, additional
meetings are necessary, I would urge that they should be held in
turn in different countries, and, if possible, in connection with
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INTERNATIONAL MAGNETIC CONFERENCE 105
existing societies, which play elsewhere the part tak£n by the British
Association in this country.
That a permanent Committee should be established is essential,
and the mode of appointing this body must no doubt be considered,
but I hope that in the course of the next few days the Committee
may be able to discuss the whole question, and that when the next
meeting of the Meteorological Conference takes place we may be
able to lay before the Committee suggestions which may lead to the
foundation of an International Magnetic Association on a stable
and permanent basis.
Another matter of great importance is the maintenance of an
international journal devoted to Terrestrial Magnetism. This we
now possess, thanks to the energy of Dr. Bauer, and I feel sure
that all present will agree that such a means of intercommunication
is invaluable. I believe, however, that the enterprise is threatened
with financial dangers, .and I desire to take this opportunity of urg-
ing all those who are interested in its success to do what they can
to support it by increasing the circulation. There is every reason
for making more use of a common journal. The records of the
observatories are necessarily so bulky that any one who desires to
obtain the facts as to the magnetic state of the earth at any given
time must collect or consult a large library of quarto volumes, in
some of which the magnetic facts are mingled with data interesting
chiefly to the meteorologist or astronomer. It is no doubt essential
that an account of all the work done at each observatory should be
published in a collected form, and that full details of the magnetic
observations should be given ; but for many, nay, for most purposes,
those who use the records will require only final results; the means
of the various elements for the year, for each month, or for any
other period which may hereafter be adopted, and the diurnal
variation, are in general wanted, rather than the hourly values. If
these means could be published together, once a year, an enormous
boon would be conferred upon magneticians. For special purposes
the theorist will have to test his views by reference to the results
published in their fullest detail; but it would be no slight gain if
the more salient facts could be compared by being placed side by
side in the same journal. One advantage such a system would un-
questionably possess. It would impress upon the authorities of
the observatories the necessity for adhering to a common form of
publication.
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io6 A. W. RUCKER [vol. in. No. 3
Some small beginnings have already been made. The Kew
Observatory' Committee now publish in the Proceedings of the
Royal Society the annual means of the elements recorded by all
the observatories which send their publications to Kew. By com-
paring two of these tables, the secular change can at once be
determined. But the system is capable of extension, not merely to
the normal values of the elements, but to disturbances. By com-
mon agreement, Greenwich and Pare St. Maur publish in each year
the records of the same magnetic storms. If this agreement
could be extended, and if the facts thus selected were brought into
juxtaposition, we might hope for a fuller and more instructive
analysis than is at present usual.
Turning from questions of organization, the primary business
of our Conference will be to discuss four questions submitted to our
Committee by the International Meteorological Conference.
The first two of these refer to the methods for calculating and
publishing the monthly means of the magnetic elements which
should, in our opinion, be adopted. I will not anticipate the dis-
cussion which will take place on these points, except to say that it
will be necessary- to bear in mind not only what is desirable, but
also what is practicable in view of the resources at the disposal of
the directors of the various magnetic observatories.
Another question deals with the relative merits of long and
short magnets, and on this point we shall have the advantage of
hearing a report on the subject by M. Mascart.
Lastly, there is a very important proposal for the establishment
of temporary magnetic observatories at certain specified places.
General Rykatchew and Professor von Bezold present an excellent
report on this subject, and I will .only remind you that, whereas the
accuracy of the mathematical expression of the magnetic state of
the earth's surface depends entirely on the number and position of
the spots at which the magnetic elements are accurately known,
the establishment of temporary observatories will be a costly un-
dertaking, for the carrying out of which all the resources at the
disposal of international science will have to be employed.
Another point of considerable practical importance will also be
brought before us. The rapid extension of electrical railways and
ways is a serious menace to magnetic observatories. From all
5 of the world we hear of observatories ruined or threatened by
nvasion of the electrical engineer. Toronto and Washington
already succumbed; Potsdam, Pare St. Maur, Greenwich, and
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INTERNATIONAL MAGNETIC CONFERENCE 107
Kew are besieged, and the issue largely depends upon whether
these great national observatories can or can not make good their
defense.
It seems to be a law of nature, ruling alike the human race and
the humblest microbe, that the products of an organism are fatal
to itself. The pessimist might infer that we are in presence of an-
other instance of the universality of the application of this law,
and that pure science is threatened by the very success of its prac-
tical applications. The smoke of our cities blots the stars from
the vision of the astronomer, who, like the anchorites of old, flies
from the world to mountains and desert places. It is only in the
small hours of the morning when
" Save pale recluse for knowledge seeking,
All mortal things to sleep are given,"
that the physicist can escape from the tremors of the traffic of a
great town.
Civilization as it spreads by aid of the means that science has
placed at its disposal is destroying records, and obliterating boun-
daries by the study of which the anthropologist and the biologist
might have read far back into the history of our race. And now
in turn the science of Terrestrial Magnetism, which, on the one
hand, is forging another link to connect the Sun and Earth, and, on
the other, is penetrating within the surface of the globe to depths
beyond the ken of the geologist, is threatened by the artificial
earth currents of the electric railway.
That the crisis is serious there can be no doubt ; but I will only
anticipate the fuller discussion which will take place by stating that
magneticians, in common with the rest of the world, recognize the
great benefit which electric traction confers upon the community at
large. We are not so foolish as to desire to embark on a crusade
against a great industrial improvement of which science may well
be proud; on the other hand, we must bold fast to the position
that provision for the conveniences which are immediately appre-
ciated by the public should be made with as little damage as pos-
sible to those studies which are not less for the ultimate benefit of
the race.
Had science, when the use of coal was introduced, been suffi-
ciently advanced to devise means for smokeless combustion, an evil,
which now in more senses than one darkens the lives of the inhab-
itants of our great towns, might have been prevented from attaining
its present gigantic proportions.
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io 8 A. IV. RUCKER [vol. in, no. 3J
We are now at the beginning of another industrial epoch, which
may indeed, if power is transmitted from a distance on a large scale,
brighten our skies, but which threatens to saturate the earth beneath
us with electric currents. That these may interfere with the gen-
eral comfort is evident from the injury which has been done to un-
derground pipes at Washington and elsewhere. The construction
of a powerful electrical railway in the immediate neighborhood of
the laboratories of a college would interfere with its efficiency, and
make it impossible to perform experiments of certain types. In
such a case, however, something could be done by arranging the
experiments to suit the conditions under which they would have to
be performed. But in the case of a magnetic observatory no such
protective measures are possible. The very object of the observa-
tory is to measure the earth's field, and if that field is artificially
altered, no modification of the methods of measurement, however
ingenious, can overcome this fundamental defect. I am glad to
take this opportunity of acknowledging that both the danger to
pure science and the necessity for obviating it have been acknowl-
edged by those who are chiefly interested in the technical applica-
tions of science; and in particular that one of the principal technical
journals, the Electrician, has supported the view that industry can
and ought to respect the necessities of research.
If, however, there be any who are inclined to ask whether the
careful study of Terrestrial Magnetism has led or is leading to any
definite results, or whether we are not merely adding to the lumber
of the world by piling up observations from which no deductions
are drawn, we may answer that, though the fundamental secret of
Terrestrial Magnetism is still undiscovered, the science is progress-
ing. In the presence of several of the most active workers I will
not enter into a detailed discussion of the tasks to which they are
devoting themselves ; I will only ask that the doubter should com-
pare a good summary of the state of the science of Terrestrial
Magnetism written fifteen or twenty years ago, such as that con-
tained in the article by Balfour Stewart in the " Encyclopaedia
Britannica," with what would be writen on the same subject to-day.
Additions would have to be made to the descriptions of the instru-
ments employed, to the discussion of the theory of the diurnal and
secular change, while such questions as the reality of earth-air
currents, and the tracing of loci of local disturbance have only been
dealt with effectively in very recent times. When, too, we compare
the older models of the magnetic state of the earth with that devised
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INTERNATIONAL MAGNETIC CONFERENCE
109
by Mr. Henry Wilde, we can not but admit, not only that a great
advance has been made in forming a simple diagram of the mag-
netic state of the Earth, but that it is possible that the model con-
tains a very pregnant hint as to the physical construction of the
Earth as a magnetic body.
The fact that Mr. Wilde has imitated the declination and dip
with remarkable accuracy all over the surface of the earth by means
of a simple arrangement of electrical currents, and by coating the
oceans with thin sheet-iron, has not attracted the attention it de-
serves. Whether the physical cause thus suggested be due to the
greater depth to which the underground isothermals penetrate be-
low oceans, the bottoms of which are always cold, or whether the
geological nature of the rocks is different below the great depres-
sions and elevations of the earth's surface, respectively, may be
open to question ; but I am persuaded that the matter should be
more fully investigated.
In conclusion, let me once more revert to the points on which I
dwelt at the beginning of this brief address. We meet with
the confidence of men who know that their science is progress-
ing, but with the mingled hopes and fears of those who still have
to deal with the great unsolved problem of the causes of Terrestrial
Magnetism and of its manifold fluctuations. This solution will be
most easily attained if we are not merely content to collect facts,
but if we so arrange them that they shall be easily dealt with. To
observe is our first duty, to organize our second ; and if these be ful-
filled, we may hope that a theory of Terrestrial Magnetism will in
the future crown the efforts, not merely of him on whom the first
glimpse of the truth may flash, but of the international co-operation
which has, by way of preparation, made " the crooked straight and
the rough places plain."
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1 10 W. VON BEZOLD AND GEN. RYKATSCHEW [vol. hi, no. 3.]
ON THE ESTABLISHMENT OF TEMPORARY MAGNETIC OB-
SERVATORIES IN CERTAIN LOCALITIES, ESPECIALLY IN
TROPICAL COUNTRIES.
Report bv Professor von Bezold and General Rykatschew.
bericht der subkom mission zur auswahl von punkten for tempo-
rAre magnetische observatorien.
Die nachstehenden Vorschlage stiitzen sich wesentlich auf eine Ab-
handlung, welche der eine der Unterzeichneten im Jahre 1897 veroffent-
licht hat. 1 In dieser Arbeit wurde versucht, durch Vergleichung mit den
Beobachtungen die Hypothese zu priifen, dass die Krafte, welche die erd-
magnetischen Erscheinungen hervorrufen, in der Erdobernache selbst ein
Potential besitzen ; auf Grund von Werthen, die ihm Herr A. Schmidt fur
je 72 urn je 5 Langengrade von einander abstehende Punkte auf 4 Parallel-
kreisen mitgetheilt hatte, gelang der Verfasser zum Schluss, dass die in
Procenten der Amplitude des Potentials ausgedriickten Abweichungen
von jener Hypothese um den 40 — 45 Grad nordlicher Breite am grossten
ausfallen, d. h. also gerade in jenen Breiten, fur welche die meisten und
besten Beobachtungen vorliegen; diese Abweichungen erreichen hier
Werth bis zu 8% der Amplitude, wahrend sie in niedrigen Breiten nur
wenige Beobachtungen vorhanden sind, viel kleiner sind, theilweise sogar
ganz verschwinden. Fur die Theorie des Erdmagnetismus ware es von
hochster Wichtigkeit, dariiber Gewissheit zu erlangen, ob dieses Resultat
nicht vielleicht durch den Mangel an Beobachtungen, besonders aus dem
Aequatorialgebiete, bedingt ist.
In derselben Arbeit hat der Autor auf Grund der von A. Schuster *
mitgetheilten Werthe eine Karte entworfen, welche fiir den Sommer ein
anschauliches Bild vom Verlaufe der Gleichgewichtslinien des Potentials
der taglichen Variation giebt ; die Darstellung der Karte bezieht sich auf
den Mittag nach Greenwicher Zeit.
Unter Annahme der Hypothese, dass die tagliche Variation ausschliess-
lich und unmittelbar durch ein unveranderliches System von Kraften
hervorgerufen wird, welche die Erde umkreisen, wiirden alle auf dem-
selben Parallelkreise belegenen Punkte auch die gleicheTagesschwankung
der Siid-Nord- und West-Ost-Componente des Erdmagnetismus besitzen.
Dieses theoretisch abgeleitete Resultat wird durch die Beobachtungen
zum Theil bestatigt ; doch liegen leider zu wenig Beobachtungen vor, um
diese Frage endgiltig entscheiden zu konnen. Ein Blick auf die Karte,
1 Sitzungsberichte der K. Preuss. Akad. d. Wissensch. zu Berlin , xviii. 1. April
1897.
1 Philos. Transactions of the Royal Society of London , vol. 130A.
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H2 IV. VON BEZOLD AND GEN R YKATSCHE W [vol. in, No. 3]
von welcher eine Copie beiliegt, zeigt uns, welch eine hervorragende Rolle
bei diesem Curvensystem die Parallelkreise 38 Grad nordlicher Breite
und 40 sudlicher Breite spielen, iiber welche die Aktiotiscentren fiir die
tagliche Periode hinwegzuziehen scheinen, so dass es vom grossten Werthe
ware, sowohl aus den diesen Parallelkreisen benachbarten Breiten, als
auch aus den zwischen beiden liegenden, d. h. aus den Tropengegenden
geniigende Beobachtungen zu besitzen.
Schliesslich wird in der citierten Arbeit auf die hohe Bedeutung hin-
gewiesen, welche detaillirte bis auf die Secunde genau gleichzeitige
Simultanbeobachtungen haben, die zu vereinbarten festen Terminen,
wenn auch nur im Laufe eines kurzen Zeitabschnittes, anzustellen waren.
Derartige Beobachtungen, wie sie auf Anregung von Herrn Professor
Eschenhagen * im Jahre 1896 versuchsweise ausgefiihrt wurden, konnen
gleichfalls nur in magnetischen Observatorien gemacht werden, welche
iiber die ganze Erde vertheilt sein mussen.
Aus diesen Griinden ware die Existenz einer Reihe von Observatorien
und insbesondere unter den bezeichneten Breitengraden besonders wiin-
schenswerth. Wenn wir aber die Vertheilung der bestehenden Observa-
torien ins Auge fassen, die auf der Karte durch schwarze Punkte be-
zeichnet sind, so sehen wir, dass bloss in Europa ein hinreichend dichtes
Netz von Observatorien vorhanden ist ; in alien iibrigen Erdtheilen treffen
wir eine deprimirende Oede an. In Bezug auf die erwahnten beson-
ders interessanten Breitengrade geniigt die Bemerkung, dass im ganzen
Aequatorialgurtel zwischen io° nordlicher und io° sudlicher Breite nur
ein einziges Observatorium, dasjenige in Batavia, besteht, und dass ferner
auf der sudlichen Halbkugel siidlich vom 35 Breitengrade gleichfalls nur
ein Observatorium (in Melbourne) functionirt ; auf der nordlichen Halb-
kugel existirt ostlich von Tiflis, zwischen dem 35 und 45 Breitengrade,
auf einer Strecke von 100 Langengraden kein einziges Observatorium,
und ebenso ist weiter ostlich von Japan auf eine Entfernung von 140
Langengraden auch kein Observatorium vorhanden.
Fiir die Untersuchung der erdmagnetischen Erscheinungen auf der
ganzen Erde, fur die Entwicklung der Theorie dieser Erscheinungen und
fiir die Priifung der bisher aufgestellten Hypothesen ist es daher unum-
ganglich nothwendig, dass die bezeichneten gegenwartig bestehenden
grossen Lucken wenigstens fur's erste darauf beschranken, eine gewisse
Minimalzahl, sei es auch nur temporarer Observatorien, zu begriinden.
Die Errichtung eines Observatoriums in Taschkent, die Wiederaufnahme
der abgebrochenen Beobachtungen im friiheren russischen Observatorium
zu Peking (resp. die Begriindung eines neuen magnetischen Observa-
toriums in Wladiwostok), sowie die Organisation von magnetischen Be-
obachtungen beim Lick- Observatorium wurden die Liicken in der Reihe
der magnetischen Observatorien um den 40 Grad nordlicher Breite er-
1 Terrestrial Magnetism , vol. i. p. 55.
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INTERNATIONAL MAGNETIC CONFERENCE
113
ganzen ; im Aequatorialgiirtel konnte die Begriindung von Observatorien
in Quito, Para, Colombo, sowie die Eroffnung der in St. Paul de Loanda
und Dar-es-Salam bereits projectirten Observatorien den gegenwartigen
ungeniigenden Zustand verbessern. Auf der siidlichen Halbkugel mussten
ausser den bereits projectirten Observatorien in Santiago de Chile und
La Plata noch ein Observatorium am Cap der guten Hoffnung und ein
anderes wo moglich auf einer der Inseln St. Paul oder N. Amsterdam
begriindet werden. Die Subkommission empfiehlt somit, ausser den be-
reits friiher projectirten, bestandigen Observatorien, sich fur die Be-
griindung folgender temporarer Observatorien zu verwenden :
1. Taschkent
2. Peking
3. Lick-Observatorium
4. Quito
5. Pari ....
6. Colombo .
7. Cap der guten Hoffnung
8. St Paul oder N. Amsterdam
Russland.
Russland.
Vereinigte Staaten N. A.
Ecuador.
Brasilien.
Anglo-Indien.
England.
Eine der grossen Seemachte,
z. B. Prankreich.
Den hier aufgezahlten sollte sich wenigstens noch ein Ovservatorium
in hoberen siidlichen Breiten anschliessen, sei es auf den Falklands-
inseln, auf Kap Horn oder an einem anderen in diesen Breiten ge-
legenen Punkte.
Im Hinblick auf die Schwierigkeiten, welche die Errichtung gerade
dieses Observatoriums bieten wird, schien es jedoch richtiger, keinen
bestimmten Vorschlag zu machen, sondern zunachst nur eine allgemeine
Anregung zu geben.
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H4 E, MASCART i vol. in. No. 3.)
ON THE RELATIVE ADVANTAGES OF LONG AND SHORT
MAGNETS.
By E. Mascart.
On employait autrefois des barreaux longs et lourds, sans doute par
l'idee que les forces agissantes elaient plus grandes et que les resultats
deyaient £tre plus surs. Les barreaux be Gauss pesaient quelquefois
plusieurs livres. La boussole de Gambey pour la declination avait un
aimant d'environ 50 cent de longueur; celui de la boussole de variations
6tait encore plus long et les aiguilles d'inclination n'avaient pas moins de
25 cent Depuis plusieurs annees on a beaucoup r£duit les. dimensions
des barreaux ; ce qui permit de rendre les instruments plus faciles &
transporter, et je crois qu'au point de vue de la sensibility on n'a fait qu'y
gagner, comme pour le compas de Lord Kelvin.
Considerons, en effet, nn barreau de forme de'terminee (tige a section
rectangulaire, par exemple). Soient
m la masse du barreau.
p son poids.
p le rayon de giration autour d'un arc transversal passant par le
milieu.
k=mfP le moment d'inertie.
M le moment magn€tique.
H la composante horizontale du champ terrestre.
D€signons par les memes lettres accentuees, m / , p*> p\ P t M', les
grandeurs correspondantes pour un aimant de mhne forme dont la lon-
gueur est / fois celle du premier. On peut admettre que l'aimantation
reste la meme dans les deux cas, quoique toute chose egale Tavantage
restera encore pour diverses raisons aux aimants courts. On aura alors
M tn p J
P J% k mp* J '
i° Si les deux aimants sont suspendus a des fils san torsion sensible,
pour determiner le produit HM, les durees d'oscillations f et / donnent
le rapport
P~HM' % k k 'AT fK
r
(I) 7-/
2 La torsion des fils de suspension n'est jamais nulle. Dans un fil
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INTERNATIONAL MAGNETIC CONFERENCE
"5
unique la section s doit £tre proportionnelle au poids du barreau (abstrac-
tion faite de l'£trier) ; par suite
s p J *
D'autre part le couple de torsion c'est proportionnel au carre* de la
section
Le rapport du couple de torsion au couple directeur magn&ique est
done
(2) 7/M == 7lM'7* := 7fMf*'
3 S*il existe un frottement dans l'appareil, comme pour les aiguilles
montees sur pointe ou les aiguilles d'inclinaison dont les tourillons rou-
lent sur des plans, le frottement est proportionnel au poids du barreau.
Le couple directeur magne*tique est lui-meme proportionnel au moment
magn&ique et, par suite, au poids. Tous les barreaux de meme forme
sont done equivalents a ce point de vue. Sans aller plus loin, exam-
inons les consequences des Equations (1) et (2). II y a tout avantage a
rendre les oscillations rapides. Si on veut les mesurer, TopeYation est
plus facile, sans avoir recours aux mlthodes compliquees de Gauss.
D'autre part, les oscillations ramortissent beaucoup plus vite et Ton n'a
pas a craindre les variations de toute nature, -telle que les defacements
du zero, pendant la serie des observations.
La remarque s'applique encore mieux aux instruments de variations
qui prennent sans retard et sans osciller la position qui convient a l'etat
actuel.
Done superiority des aimants courts.
L'equation (2) montre aussi que le rapport du couple de torsion du
fil au couple directeur magn&ique est proportionnel au cube f 1 du rap-
port de syme*trie et par consequent du poids du barreau. Toutes les
causes d'erreur qu' entrafne la suspension sont done exage'rees pour les
barreaux lourds.
On verrait de meme que les dimensions des barreaux ne jouent pas de
r61e dans les experiences de deviation pour determiner la valeur absolue
de //, puisque les formules ne dependent que du rapport des longueurs
du barreau deViant et du barreau d£vie\
Enfin les causes d'erreur £trangere, telle que la presence de petits
traces de fer dans Tinstrument ou dans le voisinage, deviennent inipor-
tants et impossibles a eliminer lorsque le moment magn£tique et la dis-
tance des poles deviennent trop grands.
A tous les points de vue il y a done inte're't a require autant que pos-
sible les dimensions des barreaux, si la precision des lectures d'angles
reste suffisante.
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1 1 6 M. ESCHENHAGEN [vol. hi. No. 3 ]
SUGGESTIONS AS TO QUESTIONS TO BE ADDRESSED TO THE
DIRECTORS OF MAGNETIC OBSERVATORIES.
By Professor Eschenhagen.
rundschreiben.
Es ist fur die magnetische Forschung sehr niitzlich, wenn ein voll-
standiges Verzeichnis aller magnetischen Observatorien nebst einer
Uebersicht der an denselben ausgeftihrten Arbeiten und Veroffentli-
chungen allgemein bekannt wiirde.
Der unterzeichnete Vorsitzende des internationalen magnetischen
Comit6s, welches von der Conferenz der Directoren meteorologischer
Institute im September 1896 zu Paris ernannt wurde, ist bereit eine
solche Zusammenstellung auszufuhren und zur Veroffentlichung zu
bringen.
Sie werden daher gebeten, die im anliegenden Fragebogen aufge-
stellten Fragen in Bezug auf das Ihnen unterstellte Observatorium zu
beantworten und denselben mit den Ihnen sonst noch niitzlich erschei-
nenden Bemerkungen mir bald wieder zukommen zu lassen.
Fragebogen.
1. Stellt das unter Ihrer Leitung befindliche Observatorium fortlau-
fend regelmassige Variationsbeobachtungen an ?
2. Werden photographische Registrirungen oder Terminbeobachtun-
gen ausgefuhrt? (Im Fall von Terminbeobachtungen bittet man die
Stunden der Ablesungen anzugeben.)
3. Welches sind die benutzten Variations- und Registrierapparate ?
(Durch Nennung des Models (z.B. Kew-Models) oder des Verfertigers zu
bezeichnen, z.B., Carpentier, Edelmann, etc.)
4. Werden gelegentliche oder regelmassige absolute Messungen
angestellt? Von welchen magnetischen Componenten, mit welchen
Apparaten, in welchen Zeitintervallen ?
5. In welchen Veroffentlichungen sind die bisherigen Resultate Ihres
Observatoriums enthalten ? Unter welchem Titel ?
Erscheinen die Veroffentlichungen fortlaufend, und unter welchem
Titel?
6. Welches sind die Werthe der erdmagnetischen Elemente und
ihrer sacularen Variation fur einen der Gegenwart moglichst nahen
Zeitpunct?
Welches ist die geographische Lange und Breite, sowie die Seehohe
des Observatoriums ?
7. Es wird um Angabe der Zeitdauer des Bestehens Ihres Observa-
toriums sowie Notizen iiber altere, nicht mehr in Thatigkeit befindliche,
benachbarte Observatorien, sowie iiber deren Publicationen gebeten.
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INTERNATIONAL MAGNETIC CONFERENCE 117
ANTRAG AUF MASSNAHMEN ZUR SYSTEMATISCHEN ER-
FORSCHUNG DER SAECULAR-VARIATIONEN DER
ERDMAGNETISCHEN ELEMENTE.
Von Dr. Ad. Schmidt in Gotha.
Bei dem lebhaften Interesse, das man in den letzten Jahren wieder be-
gonnen hat der erdraagnetischen Forschung zuzuwenden, ist zu hoffen,
dass die grossen Liicken unsrer Kenntniss von der raumlichen Verteilung
der magnetischen Kraft in nicht zu ferner Zeit wenigstens einigermassen
ausgefullt sein werden. Soil es indessen moglich sein, die zu erwarten-
den Messungen in vollem Masse auszunutzen, so muss vor alien Dingen
fur eine hinreichende Feststellung der saecularen Aenderungen gesorgt
werden, ohne die (von ihrem selbstandigen Werte ganz abgesehen) die
Reduction der natiirlich iiber viele Jahre zerstreuten Beobachtungen auf
eine bestimmte Epoche un moglich ist.
Die Bestimmung der saecularen Variationen hat auch schon bisher
stets die grosste Schwierigkeit und die Hauptquelle der Unsicherheit bei
alien Darstellungen der erdmagnetischen Kraftverteilung gebildet, und
dies wird, wenn nicht geniigende Vorkehrungen zur Beseitigung des be-
stehenden Uebelstandes getroffen werden, in Zukunft immer mehr der
Fall sein. Gegen iiber den gesteigerten Anforderungen an Genauigkeit,
die wir heute stellen miissen und bei den verfeinerten jetzigen Mes-
sungen auch stellen kdnnen, geniigt es nicht mehr, eine oft sehr ungleich-
artige Reihe von Messungen, die zufallig im Laufe der Jahre ungefahr
an demselben Orte gemacht worden sind, zusammenzufassen und dar-
aus — nicht selten durch Extrapolation — Werte der saecularen Schwan-
kung abzuleiten. Und es macht sich immer empfindlicher merklich,
wenn auf weiten Gebieten nicht einmal solche unvollkommene Mes-
sungsreihen vorhanden sind.
Nach der jetzigen L,age der Wissenschaft miissen wir es als durchaus
notwendig erachten, dass an einer nicht zu kleinen Zahl von Orten, die
moglichst gleichmassig iiber die Erde zerstreut sind, regelmassig wieder-
holte Beobachtungen aller erdmagnetischen Elemente mit verglichenen
Instrumenten und zwar stets genau an demselben Punkte angestellt
werden, um den Einfluss von lokalen Storungen auszuschliessen.
Magnetische Observatorien sind dazu natiirlich keineswegs notig ; sie
wurden anderseits, auch wenn ihre Zahl noch betrachtlich vermehrt
werden sollte, nicht ausreichen. Fur den bezeichneten Zweck geniigen,
wenigstens bis auf weiteres, viel einfachere Vorkehrungen, die bereits
einen grossen Fortschritt gegenuber dem jetzigen Zustande darstellen
wurden. Wenn etwa an jenen Punkten, die man Saecularstationen nen-
nen konnte, von Zeit zu Zeit — etwa alle 5 Jahre — Messungen angestellt
wurden, so diirfte dies zunachst durchaus geniigen. Es scheint mir eine
der wichtigsten und dringendsten Aufgaben zu sein, Massnahmen zu be-
raten, die dazu dienen konnen, dieses Ziel zu erreichen, ohne ausserge-
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1 1 8 A. SCHMIDT [Vol. hi, no 3 J
wohnliche Mittel, besonders in pecuniarer Beziehung, zu erfordern. Auf
eine solche Massnahme tnochte ich besonders hinweisen, namlich auf die
. wiinschenswerte Beteiligung der im Ausland stationierten Schiffe der
Kriegsmarinen der seefahrenden Nationen — eine Beteiligung, die man bei
dem grossen praktischen Interesse, das gerade eine zuverlassige Bestim-
mung der Saecularvariation fiir die Vorausbestimmung der erdmagne-
tischen Elemente besitzt, wohl schwerlich vergebens erbitten wiirde.
Schon jetzt werden ja vielfach die Reisen dieser Schiffe u. a. gelegent-
lich zur Anstellung magnetischer Beobachtungen verwertet; was hier
gewiinscht wird, ist weniger eine starke Vermehrung solcher Messungen,
als vielmehr eine planmassigere und nach internationalem Abkommen
geregelte Auswahl der Stationen und eine annahernd regelmassige Wie-
derholung der Messungen an geniigend vielen dieser Stationen. Gerade
dieser letztere Wunsch ist ohne Schwierigkeit zu erfiillen, da die Schiffe
der Kriegsmarinen auf ihren Reisen im allgemeinen immer wieder die-
selben Punkte beriihren. Ohne dass die sonstigen Aufgaben, denen
diese Schiffe zu dienen haben, beeintrachtigt wiirden, liessen sich daher
an zahlreichen Orten — Hafenplatzen des Festlandes wie von Inseln — die
gewunschten Beobachtungen leicht gewinnen, etwa in der Weise, dass in
einem mehrjahrigen Cyklus jeder Ort einer bestimmten Gruppe je ein-
mal an die Reihe kame. Ein international geregeltes Zusammenwirken
der Marinen der verschiedenen Staaten wiirde dabei den Vorteil ge-
wahren, dass mit bestimmt begrenzten Mitteln moglichst viel erreicht
werden konnte, weil durch eine planmassige Verteilung der Stationen
die Arbeitsvergeudung vermieden wiirde, wie sie in einer zwecklosen
Anhaufung von Beobachtungen an identischen oder sehr nahe benachbar-
ten Punkten lage.
Es ist richtig, dass durch die im vorhergehenden vorgeschlagenen
Beobachtungen nicht alien berechtigten Wiinschen entsprochen wiirde,
denn es wiirden dabei manche weitausgedehnte Gebiete keine Beriick-
sichtigung finden, so besonders die hoheren Breiten der stidlichen Halb-
kugel. Aber es wiirde immerhin ein auf anderem Wege schwer zu gewin-
nendes, wertvolles Beobachtungsmaterial zusammengebracht und dauernd
erganzt werden. Die Untersuchung jener abgelegenen, z. T. schwer zu-
ganglichen Gebiete miisste nach wie vor besonderen Unternehmungen
vorbehalten bleiben.
Auf Grund dieser, hier nur kurz angedeuteten, aber leicht weiter
auszufuhrenden Betrachtungen erlaube ich mir den Antrag zu stellen :
Das internationale Comittee moge —
1. Erwagungen dariiber anstellen, wie die Gewinnung hinreichender
Beobachtungen zur fortlaufenden Ermittelung der Saecularvariation
eingeleitet und dauernd gesichert werden kann ;
2. Insbesondere die hydrographischen Aemter der Kriegsmarinen
aller seefahrenden Staaten um ihre Mitwirkung dabei in der zuvor an-
gedeuteten Weise zuersuchen.
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INTERNATIONAL MAGNETIC CONFERENCE 119
ON MAGNETIC OBSERVATIONS IN THE AZORES.
By Albert, Prince of Monaco.
After having perceived the capital importance of the Azores, from
their geographical position, for the establishment of meteorological ob-
servatories with a view to weather predictions, I thought that these ob-
servatories might be of service to other branches of science. For in-
stance, the communications of Messrs. Neumayer, Mascart, von Bezold,
and other eminent meteorologists, to the International Conference of
Meteorologists in 1896, show that magnetic observations made at the
Azores would offer the follbwing advantages: (1) A situation near lati-
tude 40 N. (page 22) ; (2) remoteness from the permanent causes of per-
turbation of actual magnetic observation, such as electric lighting tram-
ways, and other applications of electricity; and (3) a geographical
position intermediate between Europe and America, capable of furnish-
ing most useful indications for the comparison of the magnetic curves
obtained in these two parts of the world (pp. 36 and 90).
The examination of these considerations and different interviews
which I had with M. Mascart, director of the Bureau Centrale MSteoro-
logique of France, convinced me of the advantage which would be gained
if Captain Chaves, director of the Meteorological Observatory of Ponte
Delgada, came to Europe to study the practical details of the magnetic
service there. I therefore communicated my ideas to the Portuguese
Government, who recalled Captain Chaves to undertake a mission in
this sense.
Captain Chaves, after having finished his studies at the observatory'
of St Maur under the enlightened direction of M. Moureaux, has pointed
out to me the importance of taking the present opportunity of magnet-
ically reconnoitering the archipelago, as a preliminary to the definitive in-
stallation of the observatory. This would be useful, not only to deter-
mine the value of the different magnetic elements, till now almost
unknown, 1 but besides, to determine in the island of St. Michael, which
appears likely to present conditions favorable to the installation of the
central observatory of the Azores, the locality most suitable for the com-
bined services of meteorology and magnetism.
Feeling certain that the views of Captain Chaves are just, and well
knowing his competence, being also aware that the Portuguese Geodetic
Commission finished last year the survey' of the island of St. Michael,
and that this year it will finish the survey of the neighboring island of
Santa Maria, I have resolved to undertake the charge of the above-men-
tioned magnetic reconnaissance.
1 In fact, even the value of the declination, one of the most important magnetic
elements, is given for one and the same place, Horta in Fayal, with differences
amounting to i° 22* in an interval of two years. Thus Preston in 1889 gives 25 52',
and the Acorn in 1891 gives 24 30'.
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120 /. B. CAPELLO [vol. in, No. 3.]
With this end I am now having the necessary instruments con-
structed ; and I announce to the International Commission that I hope
to be able to put Captain Chaves in the position to be able to commence
the magnetic reconnaissance of the Azores towards the month of April
of next year.
SUR LE MOUVEMENT DIURNE DU POLE NORD D'UN BAR-
REAU MAGNETIQUE SUSPENDU PAR LE CENTRE
DE GRAVITE.
Par J. B. Capello.
En combinant les variations diurnes de l'inclinaison avec celles de la
de*clinaison, sur un plan perpendiculaire a la direction de Tinclinaison,
re*sulte une courbe fermee.
Les variations ou hearts de l'inclinaison sont positives vers le sud, et
celles de la de*clinaison positives vers l'ouest.
II faut avertir que les ecarts de la declinaison doivent Stre multiplies
par le cosinus de l'inclinaison, afin de les projeter sur un plan perpen-
diculaire a la m£me inclinaison.
II est int£ressant de comparer ces courbes obtenues en divers points
ou stations du globe.
La i* rc Planche contient les courbes de Kew, Paris (Pare S l Maur),
Perpignan, et Lisbonne en 1894 et 1895.
Les courbes de Kew et de Lisbonne sont d£duites des jours tranquils
(cinq jours choisis a chaque mois), celles de Paris et de Perpignan sont
dSduites de tous les jours.
La 2^ rae Planche contient les courbes de Lisbonne et de Kew de 1896;
de S l Pe*tersbourg (1873-85) et des jours dits normaux, et celle de Lis-
bonne de 1864-72, excepte* les perturbations, d'apr£s la m£thode du
G£ne*ral Sabine.
La 3* me Planche contient les variations diurnes du Bifilaire, du ver-
tical et de l'inclinaison a Lisbonne et Kew, 1894-95-96.
Retournant a la i* re PI. on remarque que les courbes des observatoires
plus au nord sont plus rondes que celles des autres situ£s plus au sud.
Ainsi, Kew de 1894 et 1895 affectent la figure elliptique ; ensuite vient
Paris avec la forme plus allonge*e ; Perpignan encore plus £troite et mince
du cdte" de Touest, et finalement Lisbonne, dont les courbes sont plus
larges du cdte* de l'ouest, et minces de Test, affectant la forme d'un 00.
On voit un autre fait plus remarquable. Tandis que dans les courbes
de Kew, Paris, et Perpignan le mouvement vers l'ouest, du matin au soir,
est par le sud du point moyen, a Lisbonne il est par le nord, de faeon
que le mouvement est retrograde en regard des autres.
Pour mieux faire ressortir cette circonstance, nous avons dans la
2 £me pi. donne" les courbes de Kew et de Lisbonne pour l'ann£e 1896.
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I
$
a /
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122
/. B. CAPELLO.
[Vol. m. No. 3.)
Le monvement a Kew est direct (sekm les aiguilles d'une montre) ;
celui de Lisbonne est invers.
Nous avons vu (i*** PI.) que la partie de la coorbe du soir se deplace
vers le sud, an fur et a mesure que la latitude est plus petite ; on peut dire
qu'a Lisbonne le deplacement est si grand qu'il traverse la courbe du
matin.
II est facile de reconnaitre que les courbes plus ou moins rondes et le
monvement direct ou in vers dependent de la valeur diurae ou des ecarts
de Tinclinaison.
AW
$>I*r**myMJ3-M
i* — 'i fe^^v \ * — f — j
>^ — v* — rrl
2isfatu%6 J696
Ziadome/tetn
En effet, si la variation diurne de Tinclinaison est positive dans les
heures du jour (oa.-2p.) le mouvement sera direct, et au contraire sera
invers si elle est negative dans les memes heures.
Les ecarts de Tinclinaison a Lisbonne sont ne*gatifs dans les heures
(ioa.-2p.) au contraire de ceux de Kew, Paris, etc. Mais la variation
diurne de Tinclinaison depend des deux variations, ou des ecarts des
deux composantes H et V> comme il est facile de voir, d'aprds la
formule di = sin t cos * I -^ jj J.
Dans la 3* mc PI. on voit les variations diurnes des composantes
H y V, et inclinaison k Kew et Lisbonne, d'apr&s les cinq jours calmes de
chaque mois, dans les annees de 1894-95-96.
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INTERNATIONAL MAGNETIC CONFERENCE
123
On voit que les valeurs des ecarts de H a Lisbonne sont plus petites
que la moitie* des memes ecarts a Kew, et que, au contraire, les ecarts
du vertical sont plus grands que le double de ceux de Kew; quoiqu'ils
aient le meme signe, le resultat est de changer le signe des ecarts de
Tinclinaison a Lisbonne aux heures du jour (9 ou ioa.-2p.).
Afin que la forme de la courbe de Lisbonne soit semblable a celle de
Kew, il faudrait, du moins, doubler les variations de //, et require a la
moitie* celles de V.
Mtw .
2 * 44 4 #1 1 * * s»% 9 a 4 # $*%.* 4 # * m% % * 4 # a ml t 4 9 $ mf
IS96
' X € g tO % 1 4 *4J9
t * t 9 t0% t 4 9 4 nl
Nous avons fait Texp^rience, et il a rSsulte* effectivement une courbe
tr£s semblable a celle de Kew, avec le mouvement direct, etc.
On pourait ainsi attribuer ces differences aux valeurs de A", de H % et
de V, c'est-a-dire, a la mauvaise determination de ces coefficients a Lis-
bonne, mais on ne doit jamais croire qu'on puisse commettre des erreurs
si grossifcres, surtout en consid€rant qu'il s'agit des difffcrentes determina-
tions pendant une periode de 35 annees.
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124 A.SCHUSTER [vol. hi. no. 3. J
Le but nord d'un aimant suspendu par le centre de gravity, et par
un fil sans torsion, devrait decrire sur un plan perpendiculaire k leur
direction une courbe egale ou tres semblable k celles des i irc et 2* m « PL
Un barreau magn€tique cylindrique et creux devrait £tre suspendu
par le centre de gravity, muni de lentilles ou de miroirs, de facon que tous
les mouvements seraient enregistres sur un papier photographique place"
sur un plan perpendiculaire k la direction de l'inclinaison, et ce papier
devrait £tre disloque" rapidement k la fin de chaque heure par une certaine
quantity, afin que les traces ne seraient embrouillees.
Je pense qu'un instrument semblable serait difficile k construire,
surtout en consequence de la petitesse des mouvements, mais il pourrait
faire de bons services k la science du magn€tisme terrestre.
ON A SIMPLE METHOD OF OBTAINING THE EXPRESSION OF
THE MAGNETIC POTENTIAL OF THE EARTH IN A SERIES
OF SPHERICAL HARMONICS.
By Arthur Schuster, F. R. S.
The methods which have been employed so far to represent the earth's
magnetic potential in a series of spherical harmonics suffer from the
serious defect that the different coefficients are not determined indepen-
dently of each other. Thus, in the latest and most accurate computation
of Adolf Schmidt, the value of the first and largest coefficient was found
to be 1,872, 1,913, or 1,921, according as the expansion is supposed to
end with terms of the third, fifth, or seventh order respectively. If the
value of the potential were known at all points of the earth's surface, it
is well known how, by a direct integration over the surface of the sphere,
each coefficient may be separately determined. But there are large tracts
of the earth over which the magnetic forces have not been directly ob-
served, and hence some form of interpolation is always implied in what-
ever method is employed. A certain amount of uncertainty results from
this interpolation ; but perhaps less than is commonly supposed, owing
to the fact that neglecting magnetic masses actually situated in the sur-
face, the potential and all its different coefficients must be continuous.
A complete knowledge of the potential over any finite part of the earth's
surface is therefore theoretically sufficient to fix it all over the globe, and,
at any rate, the continuity of the potential and of its derivatives facilitates
and justifies the process of interpolation.
The whole interest of the expansion in a series of spherical harmonics
centers round the first few coefficients. It would be waste of labor to
obtain a complete representation of the potential, as we know that a very
large number of terms would be necessary for the purpose. The sole
object of the expansion can only lie in the separation of the outside and
inside forces, and for the present, at any rate, our interest in the outside
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INTERNATIONAL MAGNETIC CONFERENCE
125
forces must be confined to the first few terms. Hence I consider it a
matter of great importance to obtain these terms separately in such a
way that their value does not depend on the number of terms which are
taken into account. I believe the following method to solve the difficulty.
I write P n for the zonal harmonic, T„ a for the tesseral harmonic de-
fined by
where to is the colatitude and /* = cos #.
If it be required to represent a function V, of H and the longitude A y in
a series of spherical harmonics, it is known that the coefficients will de-
pend on integrals of the form
/
VT H ° cos aA dw,
ut being a surface element. The method I propose depends on a trans-
formation which will allow the above integral to be expressed as a finite
sum of integrals having one of the forms :
%/ O J O
Vcosp#cos<rA dSdA,
%/ o */ o
or
I I V sin pS cos <rA d6dA.
J o •/ o
In other words, if V is expressed in a series the terms of which are of
the form cos pB cos cA or sin p6 cos <rA t and if equations are obtained once
for all to give cos p& or sin po in a series of tesseral harmonics, the
problem of expansion is solved, though the independence of the higher
and lower terms is not necessarily secured. The first step of the pro-
cedure which is common to all methods consists in expressing V in the
form
V= F Q -f F t cos A + F 2 cos 2A + . . . )
+ .F I / snU+ .F/sin 2A+ . . . J • ' • (0
where F and F f are functions of the colatitude. If V is given discon-
tinuously ; as, e.g., if it isjknown at the points of intersection of a number
of latitude and longitude circles, each latitude circle will give an equation
of the above kind. If the number of such equations is sufficient, the
values of F and F* may be plotted in terms of 0, and by calculation or
mechanical integration we may obtain the values of F and F / either as
a series
F a = a -f a x cos H + a 2 cos 2# -f .... (2)
or in the form
F„ = dj sin H -f 6 2 sin 2H + (3)
Only one of these forms is useful for our purpose, as I proceed to show.
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126 A. SCHUSTER [Vol. Ill, No. .3.]
If a be even, T n G may be expressed in the form of a finite series of
the form
T n ° — a n cos nH -f a H _ 3 cos (n — 2)0+ . . .
Hence, if <r be even
r.
T n ° cos pQdH = o if p > n\
and the integral will also vanish if p -f n is an odd number. It follows
that for <r even
f + T» sinpVdfi =ij*T n a [cos (p + 1) — (p— 1) 0] rf#
= o if / > » or if (P 4- w) is an even number.
It follows that (<r even) we may obtain a number of series in which
the sines of multiples of 8 are expressed, as in the following scheme,
where the numerical coefficients are left out for the sake of simplicity : —
sin0 =V + V +2 + • • •
sin 20 =7;%, + T a \^ . . .
sin** =V4i+V +J + • • • ) (4)
sin^-j i)tf= 37% a+ • • •
sin/W = 7> +I + 7>% 3 + . .
Whenever / is smaller than <r the series begins with the term T ° or
7* * . , , according as p be odd or even ; but when p is larger than <s the
series begins with 7^% , .
If, therefore, F G be expanded in a series of sines, as indicated in (3),
the sine functions may by (4) be expressed in tesseral harmonics, and
each coefficient of T„ a in the final representation of Fwill only depend
on n - ; coefficients of the sine series if n is even, and on coeffi-
cients if n be odd. Thus, the first coefficient, which is of the third de-
gree, only requires one coefficient in the series of sines, and will be inde-
pendent of all the others.
For the simplest case a— o; equations (4) resolve themselves into
the wellknown ones :
Um0 = P o - 5 g P 2 -^P 4 -... V
U a2 H= 3 P,- 7 -P i -^P 5 -...!
3 2 • a D 45
• sin*"- ' °
(5)
3,-3»-5/».-=S'»4
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INTERNATIONAL MAGNETIC CONFERENCE 127
Hence, to expand a function into zonal harmonics, we may, if chief
attention is to be directed to the first few terms, express it in a series ot
the sines of multiples of 0, and substitute the above values. P only
occurs in the first equation, P x only in the second, P 2 only in the first
and third, and so on.
We may show in a similar manner that if a is odd, we must use (2)
(the cosine form of the series) for F a .
For the expansion of
d°P
T H a sin V = sin ff + » -. - w
= n + I cos(7i-f i)#-r a n -i cos(n— i)tf-f . . .
leads to the conclusion that
T»° cos pSdfji = o when p > n ~x 1 and when p -f n is even.
We find thus for <r = 1
I icos2w=- 3 r I ' + Jr/ J -/ 2 |7- 5 ' ... ( . . . . ( 6)
^cos 3 *= -57-,' + ^ 7"/ + . . .
--cos 40; 7^' + - r s '+ . . .
where T/ will only occur in the first and third equations ; and generally
a term of degree n will occur in - equations if n be even, and in
equations if n be odd.
In the case of the magnetic potential the quantities which are directly
observed are the forces which are connected with the potential V by the
relations
v W v • u dV
*=- *sintf=^ (7>
the radius of the sphere being, for simplicity's sake, taken as unity.
\X=. force to north ; Y= force to west ; X = longitude measured east-
ward.]
If Y sin 8 be expanded in a series of surface harmonics the potential
V will be obtained immediately in a similar series ; but somewhat diffi-
cult complications arise when V is to be obtained from the series for X.
This difficulty completely disappears in the method here proposed for X
being expressed in a series of circular function, we may integrate with
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128 S. LEMSTROM [Vol. m. No. 3]
respect to B without changing the nature of the series. The process to
be employed may be summed up as follows : —
Express both X and Y in the form —
X=X + X 1 COSX + Jf 2 COS2,l+ . . .
+ X/ sin X -f X 2 ' sin 2X + . . .
Y= y, cos X + Y 2 cos 2* + . . .
+ Y/ sin X + K/ sin 2X + . . .
and further express A^ and K ff in Fourier's «wfo* series for even and in
the sine series for a odd. If V is then calculated by either of the equa-
tions (7) and the substitutions, or (5) or (6) of the corresponding equa-
tions are performed, the potential will be expressed in a series of spher-
ical harmonics. The values of X and Y are not known in the polar region,
but must be obtained by interpolation. The term interpolation is the
appropriate one because the value of X a and Y a are known at the poles,
vanishing there except for Y x . Also the first <r differential coefficients
of X a and the first <r — 1 differential coefficients of Y a will vanish at the
same points. The value of Y x and Y/ is very approximately known at
the poles from previous investigations, and also its first differential coeffi-
cients will vanish.
I have not taken account of the possibility of earth currents travers-
ing the surface of the earth in sufficient intensity to affect magnetic
forces. The investigations of Adolf Schmidt have shown how the prob-
lem must be treated when their influence has to be taken into consideration.
The general method of expansion here suggested will remain the same.
ON THE RELATIONS BETWEEN THE VARIATIONS IN THE
EARTH CURRENTS, THE ELECTRIC CURRENTS
FROM THE ATMOSPHERE, AND THE
MAGNETIC PERTURBATIONS.
By Selim Lemstrom.
The paper contains an historical sketch of the observations and
researches made on the earth currents by Lamont, Airy, Wild, Blavier,
and others. The author describes the method employed by him for
measuring the electro-motive force of the electric currents coming from
the atmosphere, and gives the evidence of the fact that the variations 01
earth currents occur a short time (five minutes) before the magnetic
perturbations, and that the former are more numerous than the latter.
From the observations in Sodankyla it is, however, proved that all mag-
netic perturbations are not preceded by variations in the earth currents,
but that these probably are caused by electrical currents from the atmos-
phere to the earth, or vice versd.
The proofs of that conclusion are: (1) That the magnetic perturba-
tions in polar regions have a contrary direction to those in more southern
countries; (2) That at the times of auroras the electrical current from
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INTERNATIONAL MAGNETIC CONFERENCE 129
the atmosphere varies much, and must exert on magnetic instruments a
marked influence depending on their position, relative to the space within
which this current is moving. It follows from this that we can not find
the causes of the magnetic variations, or, rather, perturbations, before
we have investigated the earth currents and the electrical currents in the
atmosphere.
The author's experience shows that we must seek the key to these
relations in the polar regions. Researches have shown that the magni-
tude of these variations of the earth currents increases with the latitude
in a very high ratio. When the diurnal variation in Pawlowsk has a
value of o, 0008 volt, it rises in Sodankyla (7 more to the north) to
o, 0600, or 75 times more. Moreover, we find from the lately-published
third volume of the observations from the international polar stations at
Sodankyla and Kuttala that the earth currents as well as the electric
currents in the atmosphere depend intimately on the belt of the maximum
polar light. It will be very clearly seen that we also have a maximum
belt of the earth currents and even of the currents in the atmosphere. The
paper finishes with a proposition that the International Conference on
Terrestrial Magnetism and Atmospheric Electricity should discuss the
two following questions: What significance must be attributed to the
earth currents and the electric current from the atmosphere in the ex-
planation of the causes of magnetic perturbations? What is to be done
for the further investigation of the connection between the magnetic
perturbations and the electric currents ?
The author also proposes that the International Conference should
take steps for establishing two international polar stations, one in the
North of America, the other in the North of Europe, both situated in
the southern border of the polar light maximum belt. In connection
with both these principal stations there should be a northern by-station,
in which, as well as in the principal stations, all the magnetic variations,
the earth currents, and the electric currents from the atmosphere, be-
sides all meteorological observations, should be made simultaneously,
and with self-registering apparatus of the best construction, the details
of which ought to be stated by the International Conference.
In connection with these observations it ought to be expressed as
desirable that all magnetic observatories should, if possible, establish
similar observations with as identical instruments as possible. Since
the researches of the electric currents from the atmosphere require
points elevated about 400 m., it seems difficult to unite these observa-
tions with those in an observatory. We, however, must remember that
the electrical resistance in the circuit, from the earth to the atmosphere,
is so great that one can put in several miles of wire without any sensi-
ble augmentation of it. It is well understood that the mountain on
which an apparatus for out- or in-streaming of electricity is placed can,
without serious damage, be far away from the observatory.
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130 A.SCHUSTER ivol. hi, No. u
ON THE INTERPRETATION OF EARTH CURRENT OBSERVA-
TIONS.
By Arthur Schuster, F. R. S.
If two metallic plates are inserted into the ground and connected by a
wire, an electric current is found to traverse the conductor, and this is
generally called the "earth current." It is not, however, obvious at first
sight what the connection is between this observed current and that
which traverses the ground when the earth plates are removed. The
statement sometimes made that the observation gives the difference of
potential of the earth at the two points at which the plates are inserted,
would be true, provided the connecting wire has a sufficiently large resist-
ance, if earth currents were only due to chemical or thermo-electric
forces. But as there can be little doubt that earth currents are chiefly,
if not entirely, effects of induction, a separate investigation is necessary
as to the interpretation to be attached to the galvanometer indications.
Let A and B be two points in a line of flow of the currents traversing
the earth, and consider a tube of flow passing from A to B. The spe-
cific resistance of the ground being />, let p be changed to p' for the
material inclosed by the tube. I determine in the first place the effect
of this change of resistance on the distribution of currents. The change
of resistance could be counterbalanced by an electric force — (p — p') u
acting throughout the tube, where u is the density of the undisturbed
currents, and it is therefore equivalent to the introduction of an electro-
motive force I (p — p')udl in the tube of flow, dl being an element of
its length and the integration being extended from A to B. If p and u
are constant within the tube, the additional current flowing through it,
owing to the change of resistance, will be —
(p-pya
x+s
where /? denotes the resistance of the tube, and S the resistance of the
ground between A and B. If the resistivity p / is of the order of magni-
tude of that of copper, it will be small compared to />, and may be neg-
lected in the above expression.
Imagine now this tube of flow between A and B to consist of two
overlapping tubes, one of material equal to that of the rest of the ground,
the other of copper, and let the latter tube be lifted out of the ground
without altering its total resistance, but keeping its connection at
A and B. The current traversing the lifted-up part will remain the
same as beforeTprovided {hat the electromotive forces of induction are
not sufficient to produce a3 appreciable current in a circuit made up of
the original and displaced positforf of the tube, a condition which will be
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INTERNATIONAL MAGNETIC CONFERENCE I3I
satisfied in the case of earth currents, except perhaps at times of great
magnetic storms.
We have now an arrangement equivalent to that used in earth-
current observations, for the only effect of the earth plates at A and B
will be to diminish the earth resistance S.
The observed current i will be connected with u by the relation
.__ pul
% ~~RVS
The resistance R -f- S is measured by the introduction of an electro-
motive force e in the circuit ; if the observed current, under these circum-
stances, be increased by a quantify ?> the equation
ei
w = — 7?
will give the current density of the earth current. It is seen that u is
proportional to the conductivity of the material of which the ground is
made up, and that a knowledge of that conductivity, which may vary
from day to day, according to the amount of moisture contained in
it, is therefore essential to a correct interpretation of earth-current
observations.
If the circuit is a long one, S may be small compared to R, and the
latter quantity will be ^-, a being the cross section of the wire, so that
a p
which shows that the current densities in the wire and ground are in the
proportion of their conductivities.
The above investigation points to the importance of measuring the
conductivity of the ground wherever earth-current observations are
made. Samples of the soil taken from different depths would probably
give different results, and would then indicate how the current density
varies with depth.
THE MAGNETIC AND ELECTROLYTIC ACTIONS OF ELECTRIC
RAILWAYS.
Electric Railways and Tramways.
[For the following abstracts we are indebted to the British Western
Daily Press, of September 16th. — Ed.]
There was a joint discussion with Sections A and G and the Interna-
tional Magnetic Conference on the Magnetic and Electrolytic Actions of
Electric Railways. It was opened by Dr. Schott, of the United States
Government, who described the effect electric railways had had on mag-
netic observatories of the United States. It was proposed to move them
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I3 2 INTERNATIONAL MAGNETIC CONFERENCE [vol. hi. No. 3.]
elsewhere, and he calculated they would have to be a distance of three
miles from the electric tramways to avoid the disturbance.
Professor A. W. R&cker, secretary of the Royal Society, showed
some diagrams evidencing the effect produced on the declination of the
needle made by the South London Electrical Railways. One illustrated
the effect on the needle half a mile from the railway in a house carefully
chosen at a distance from any great highway, so that the disturbance
could not be said to be from passing traffic. There was a continual
backwards and forwards movement of the needle, and on occasions a
complete displacement of the whole line through a considerable distance.
Another diagram showed the effect produced at Chelsea, at a distance of
two and three-quarter miles from the electric railway. A curious fact
was that the disturbance died down at eleven o'clock at night when the
trains ceased to run, and when the trains began to run again at six
o'clock in the morning, the disturbance was again produced. Almost
the same effect was also shown to be produced at the observatory at
South Kensington, about three miles and a half from the electric rail-
way. This would entirely ruin the magnetic results of the observatories.
At Greenwich the effect on the earth currents made the record worthless
from every point of view. What was to be done ? They could not stop
electric railways and tramways. They must meet those engaged in pro-
viding them if they would meet them, and so far they had met them in
a very friendly manner. The two causes of the disturbance were indi-
rect electric magnetic effect, and the effect of earth currents. The rem-
edy for earth currents was that the return rails should be insulated, and
they had also suggested that the distance between conductors should not
exceed one-hundredth of the distance of the conductors from Kew Ob.
servatory. These two conditions had been incorporated in a bill for the
establishment of an electric tramway in the neighborhood of Kew. If
electric railways could be made less dangerous by other means these
conditions would not apply.
Mr. W. H. Preece, F. R. S., treated the subject from another point of
view. They had considered the troubles and disturbances produced in
magnetic "observatories." Those observatories had existed for centu-
ries, and were bound to be protected. There were also other applications
of magnetism and electricity that had become vested interests. Tele-
graphs had been in use for over sixty years, and telephones for twenty
years; and in his position as a public official he had been obliged to
watch the introduction of those different forms of industry dealing with
electricity, somewhat as a cat watched a mouse. The post-office had es-
tablished in different parts of the country observing circuits, and since
the South London Electric Railway was established they had been keep-
ing a very close watch on what had been going on. These disturbances
were not alone due to the use of the earth, but there were also great dis-
turbances due to electric-magnetic induction. Currents of one hundred
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INTERNATIONAL MAGNETIC CONFERENCE
*33
amperes would produce a disturbance at a distance of nineteen miles.
This had led him to pursue the subject of wireless telegraphy. The
second disturbance was due to the moving of magnetized masses of iron,
and the third, in his opinion, the most serious of all, was the disturbance
due to leakage. The whole of London had now been carefully explored,
and had been found to be disturbed by currents on the City and South
London Railway, which at one time produced currents greater than the
working currents of the telegraph, and, therefore, disturbed it altogether.
This showed that the currents at that time were very badly insulated,
and he believed that in no single instance had any fault showed itself
that was not remediable. If all telephones had a metallic circuit and
twisted conductors they would be found very free from disturbance.
The disturbance of the telegraphs was only a serious thing because the
disturbance was caused by such an imperfect machine as that of the
City and South London Railway, which was made before the present
Board of Trade regulations were in force. A leakage from the electric
light station at Deptford some time ago was felt all over London, and
dangerously affected the working of the signals on the Southeastern
Railway ; but that had been entirely remedied. So far as railways were
concerned the first remedy was to bond the rails, but experiments
showed that that was not completely effective. In that town (Bristol) it
was suggested by Major Cardew to apply opposition pressure, as it were,
to different parts of the earth so as to retain the return conductor at a
uniform potential. This had certainly had a beneficial effect. Before
that was done the disturbance in Bristol was very serious, but this
method had brought them down to very small limits. From measure-
ments made in June last, the magnetic disturbance only slightly ex-
ceeded one volt on the two ends passing though the post-office. Those
who carried out these new works must see that the earth could not be
handled with impunity. The earth was the vested interest of the whole
nation. The earth was really a poor conductor, and it was very much
better to dispense with its use altogether. Anyway, the use of the earth
was a special right of the public, much more was it the right of scien-
tific observers, and its acquisition by force by these great electrical in-
dustries was to be resisted. (Applause.)
Professor Silvanus Thompson said if they would only use alternat-
ing currents, and employ no earth return, the difficulty would be at an
end. He thought they were fighting a phantom.
Professor REcker said they were quite aware that with the systems
these disturbances might be lessened; but at present they had to
defend themselves against dangers which existed.
Dr. Eschenhagen exhibited photographs showing the character of
the disturbing influences of electric tramways.
Signor L. Palazzo also addressed the section on this subject.
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i 3 4 INTERNATIONAL MAGNETIC CONFERENCE (vol. iii, No. 3 .^
The Corrosion of Water and Gas Pipes by Return Currents.
Dr. J. A. Fleming, F. R. S., next made a communication " On the
Electrolytic Corrosion of Water and Gas Pipes by the Return Currents
of Electric Tramways/' The Board of Trade regulation affecting this
matter was as follows : " If at any time and at any place a test be made
by connecting a galvanometer or other current indicator to the insulated
return, and to any pipe in its vicinity, it shall always be possible to
reverse the direction of any current indicated by interposing a battery
of three Leclanche cells connected in series if the direction of the cur-
rent is from the return to the pipe, or by interposing one Leclanche cell
if the direction of the current is from the pipe to the return." The
above, translated out of official language, signifies that if the pipe is neg-
ative to the rail the potential difference shall not exceed 4*5 volts, and if
the pipe is positive to the rail the potential difference shall not exceed 1*5
volts. Assuming then that the Board of Trade regulations are obeyed,
the chief question of practical interest at present is to determine whether,
under normal conditions of working, a potential difference of less than
1*5 volts between a pipe and the nearest part of an earth return, the pipe
being positive to the return rail, is sufficient to cause an injurious action
on the pipe by the production of electrolytic erosion. Experiments car-
ried out showed that there is no absolute security in the limit of 1 %
volts as imposed by the Board of Trade regulation. 1
The president, Professor Ayrton, in closing the discussion, said he
was not aware of any train or tram worked by alternating currents. It
was, therefore, right they should consider the dangers connected with
the employment of a system certain to be adopted. For several years
he had been urging that the present method of construction and working
of electric railways and tramways must ultimately be relegated to the
list of makeshift contrivances. Dr. Fleming had pointed out that the
Board of Trade regulations do not fulfill the objects intended ; namely, the
preservation of the water pipes. He (the president) had advised gener-
ally the insulation of the return conductors, not merely because one hoped
to save the possibility of carrying out magnetic work, but because he
believed it was to the interest of the tramways themselves to use insu-
lated returns; and Dr. Fleming had now strengthened his argument
immensely.
1 Professor Fleming's paper will be found in full in the Electrician, September
16, 1898, page 6S9
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LETTERS TO EDITOR
ESCHENHAGEN'S ELEMENTARY MAGNETIC WAVES.
The recent observations of Eschenhagen seem to have shown that
his delicate magnetic needles oscillate in regular periods, sometimes in
12 or 15 seconds, but more frequently in 30 seconds. The normal rate
of vibration of his needle in an undisturbed field is about 8 seconds.
Experiments made with other needles gave similar results ; but these
also had a normal periodic vibration in 8 seconds. He concludes that
these 30-second vibrations represent fundamental normal phenomena of
terrestrial magnetism.
Those who recognize the possibility that electromagnetic waves
emanate from the Sun, or that they in general permeate the space
through which the Earth is traveling, must expect to find waves of very
various preriodic times affecting the Earth simultaneously, and in addi-
tion to periodic impulses there may sometimes occur non-periodic and
violent impulses, which, however, may possibly be analyzable groups
of concurrent waves. In order to detect the presence of complex com-
binations of waves, we need some arrangement that shall analyze such a
group into its elements just as the prism analyzes the groups of short
visual waves, or just as a series of resonators analyzes a complex group
of acoustic waves. This same principle of a resonator was recently ap-
plied by J. Wilsing and J. Scheiner. (See Wiedemann's Anna/en, Bd.
LIX, p. 782, and also Astronomische Nachrkhten, Band 142, No. 3386.)
Their results were negative, and indeed, as was remarked by Professor
John Trowbridge {Monthly Weather Review, November, 1896, Vol. XXIV,
p. 409), " It is doubtful if such radiations can be detected by their ar-
rangement unless it is made extraordinarily sensitive, in which condi-
tion it would be affected by slight jars and mechanical vibrations One
should repair to an isolated mountain peak to carry out such experi-
ments."
An equivalent, but possibly more sensitive arrangement is the deli-
cate magnetic needle when its indications are properly interpreted. A
needle that has a normal period of vibration of 8 seconds is equally sen-
sitive to all impulses or waves whose periods are harmonic with it, espe-
cially those of 1, 2, 4, 8, 16, 32, 64 seconds interval, while one having some,
other normal periodic time will be equally sensitive to its own harmonic
set of waves. The fact that an 8-seconds needle, or strictly-speaking a
7.5-seconds needle, oscillates quite regularly in intervals of 30 seconds,
merely demonstrates that it received impulses at regular intervals such
as forced it from its normal 7.5 into its actual 30-seconds vibration, and
these outside impulses must have come to it at regular intervals 01
135
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136 LETTERS TO EDITOR TVol. m. No. 3-)
either 7.5 or 3.75 or other smaller subdivisions of the normal period. By
the cumulative influence of these impulses the needle may be forced to
make a large oscillation, even when the individual impulses are quite
feeble, so that in this case the needle is more sensitive or rather more
valuable than the apparatus of Wilsing and Scheiner.
If now we enlarge our magnetic apparatus into a battery of a hun-
dred such needles, each having a normal period slightly different from
its neighbor, and representing a given set of prime numbers, we shall
bz able to detect the presence of a large variety of periodic electro-
magnetic impulses. It is fair to presume that such a variety of im-
pulses is always present in the terrestrial magnetic field, but I know of
no reason to suppose that any special rate of vibration should occur at
one time more than at another. The oscillations of Mr. Eschenhagen's
magnet simply prove that on certain days and hours its particular har-
monic wavelength happened to occur, and when his magnet made no
record we may presume that other magnets having different periods
would have done so.
Instead of a cumbersome arrangement of numerous magnets it would
be simpler, and certainly very interesting, to attach a small bit of copper
to his 8-seconds magnet so as to slightly alter its moment of inertia, and
therefore its time of vibration. If the small mass be adjustable, one
might by experiment so adjust the needle at any moment that it will
respond to some other vibration ; that is, the one active at the station.
United States Weather Bureau. Cleveland Abbe.
The following reply to Professor's Abbe's criticism has been received
by the editor :
" In meiner Abhandlung 1 ist der Beweis erbracht, dass mein aperio-
'disches Instrument auf kiinstliche Schwingungen reagirt ohne in Eigen-
schwingungen zu gerathen. Inzwischen habe ich erfolgreiche Versuche
gemacht, allerlei verschiedene Perioden kiinstlich durch Drehen von
Magneten hervorzubringen. Der Apparat zeichnet alle auf, ohne in
Eigenschwingungen zu gerathen. Dasselbe thut iibrigens auch die
Natur. Es kommen alle Perioden von etwa 12 sec. an aufsteigend vor
bis 1 00 sec. und mehr.
Es erscheint nun gar nicht nothig sich die Aufgabe so zu stellen
wie Herr Professor Abbe, namlich viele Instrumente von verschiedener
Schwingungsdauer aufzustellen, sondern nachzuweisen, dass ein Instru-
ment auf alle mogliche Perioden reagirt.
Wir verfolgen jetzt die Sache mit neuen, noch empfindlicheren
Apparaten mit bestem Erfolg. Ich denke fur Bristol eine Mittheilung
auszuarbeiten." M. Eschenhagen.
Potsdam, 5. Juni, 1898.
»Cf. Vol. n, pp. 105-114.
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EDITORIAL ANNOUNCEMENT.
It is with great pleasure that I am able to announce in this number that
I shall hereafter have the co-operation of Professor Thomas French, Jr., in
editing and publishing the Journal.
Professor French has been in charge of the Department of Physics of the
University of Cincinnati since 1883. He is a graduate of Harvard, and re-
ceived the degree of Ph. D. from Heidelberg in 1876. In planning the new
physical laboratory of the Cincinnati University, to be built during the ensu-
ing year, through the generosity of the Honorable Briggs S. Cunningham, of
Cincinnati, Professor French is making every effort to provide for a labora-
tory especially adapted to investigations in terrestrial magnetism.
I had intended to withdraw from the chief editorship of the Journal
upon the completion of the present volume. The duties devolving upon
me had become so manifold since it was founded as to make it utterly impos-
sible for me to look after its interests successfully. Printed announcements
of this fact were prepared, and were to have been inserted in the June issue
of the Journal. Owing to the solicitations of friends, especially of Professor
French, I postponed the matter for further consideration.
Now, with the assistance promised by Professor French, and with the
co-operation of all interested in Terrestrial Magnetism and the periodical
devoted to it, I look forward to a brighter future for the Journal.
The need of a journal of this kind as a medium for intercommunication,
and the desirability of the earnest support of all interested in its success, are
well set forth in Professor Riicker's address, printed in this issue.
It is hoped that some favorable announcements can be made in the next
number by which it will be possible to still further increase the Journal's
sphere of usefulness. L. A. B.
NOTES.
Course in Terrestrial Magnetism at the University of Cincin-
nati. — Professor Bauer will give, during the present year, in co-operation
with the Department of Physics, a course of lectures on " The Theory and
Practice of Measurements in Terrestrial Magnetism." The course will con-
sist of measurements of the magnetic elements in the field, the reduction and
the discussion of magnetic observations, the theory of the potential function
as applied to the earth's magnetic phenomena, and the solution of some def-
inite problem to be assigned each student.
Course in Terrestrial Magnetism at University of Wisconsin.—
Professor John E. Davies, who occupies the chair of Electricity, Magnetism,
and Mathematical Physics at the University of Wisconsin, offers a special
course of lectures upon Terrestrial Magnetism during the Fall Semester of
this year. Part I will be non-mathematical, and will discuss our present
knowledge of the distribution of magnetism over the earth's surface ; its sec-
ular and other variations, and the various explanations which have been sug-
gested for them ; the objects and equipment of magnetic observatories ; the
probable connection of magnetic changes with solar disturbances and the
137
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1 38 RECENT PUBLIC A TIONS. [vol. hi, no. 3]
weather, and similar questions. Part II will treat of the theories of magnet-
ism, the magnetism of iron ships, shops, electric railways, rocks, and the so-
called magnetic shielding. Whatever mathematics may be necessary will be
used in the discussions of this part of the course. The whole mathematical
development of the subject up to the present time will be historically out-
lined also, if time permit.
RECENT PUBLICATIONS
Abbe, C. The Origin of Atmospheric Electricity. Month lv Weather Review,
Vol. XXVI, No. 172, Pp. 259 and 260.
Borgen, C. Zur Lehre von der Deviation des Kompasses. Ableitung des
Ausdrucks fiir die Schwingungsdauer einer unter dem Einflusse eines
beliebig gelegenen Magnets stehenden Nad el. Aus dem Archiv der
Deutschen Seewarte. XX Jahrgang 1897. No. 1. Hamburg, 1897.
Pp. 21.
Durward, Arthur. On the Temperature Coefficients of Certain Seasoned
Hard Steel Magnets. Repr. American Journal of Science. Vol. V, 1898.
Pp. 12.
KELLER, F. Ulteri6ri Recerche sull' Intensita Orizzontale del Magnetismo
Terrestre nei Pressi di Roma con note che riguardano le condizioni geo-
fisiche delle localita esplorate. Frammenti concernenti la Geofisica dei
Pressi di Roma. N. 7. Roma, 1898. 19 x 27 cm. Pp. 19.
Klossovsky, A. Annales de V Observatorire Magn6tique et M£teorologique
de rUniversite" Imperiale a Odessa pour 1897. Odessa, 1898. [Pp. 1-19:
Observations astronomiaues et magne'tiaues en 1807 par P. Passalsky.
PI. 1. Marche diurne des elements magnetiques a Odessa, 1897.]
HepiTES, S. C. Analele Institutului Meteorologic al Rom&niei. Tomul XII,
Anul 1896. Boucarest and Paris, 1898. [No. 7, Pp. 161- 179; Observatoire
me'teorologique-magn£tique de Pawlowsk par D. Bungetzianu.]
Lagrange, C. Un Pdle Magn£tique Local en Europe. Ciel et Terre, ler Juin
1898, No. 7. P. 168.
Mathias. Magnetic Charts. "Jour, de Physique," August; abstracted briefly
in Ivond. "Elec," September 2. [The autnor proposes a magnetic chart
for France, on which are to be entered, not the magnetic elements for the
time being, but the difference between the local elements and those of the
central observatory.]
Nordenstroem. Magnetic Surveying for Iron Ores. Lond. "Elec. Eng.,"
September 2. [Reprint of an illustrated paper read before the Iron and
Steel Institute in Stockholm. In Sweden magnetic instruments have long
been employed on a large scale for discovering iron ores, and the instru-
ments have reached great perfection. — Electrical World, Sept. 24, /tfo.v.]
Newcomb, S. An Unusual Aurora. Science, Vol. VIII, No 195. September
23, 1898. Pp. 410-41 1.
PEIRCE, B. O. On the Induction Coefficients of Hard Steel Magnets. Repr.
American Journal of Science, Vol. II, November, 1896. Pp. 8.
Peirce, B. O. On the properties of Seasoned Magnets made of Self-hardening
Steel. Repr. American Journal of Science, Vol. V, May, 1898. Pp. 9.
Stevens, J. S. An Application of Interference Methods to a Study of the
Changes produced in Metals by Magnetization. Repr. Physical Review,
Vol. VII, No. XXXV, July, 1898. Pp. 8.
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Volume 111 Nut Y e r$t J IClT*%°H
Terrestrial Magnetism, December, 1898.
REPORT OF THE PERMANENT COMMITTEE ON TER-
RESTRIAL MAGNETISM AND ATMOSPHERIC ELEC-
TRICITY TO THE INTERNATIONAL METEOROLOG-
ICAL CONFERENCE.
Constitution of the Committee.
I. The Committee on Terrestrial Magnetism and Atmospheric
Electricity, appointed at Paris in September, 1896, consisted of
eight members. These gentlemen found that it was desirable to
add to their number, by co-option, and the constitution of the Com-
mittee is now as follows :
Appointed at Paris — Professor Riicker (President), Professor
Eschenhagen, Professor Liznar, M. Th. Moureaux, Sig. L. Palazzo,
Dr. Paulsen, Dr. van Rijckevorsel, General Rykatchew.
Co-opted — Dr. Bauer, Professor W. von Bezold, Sig. Brito Ca-
pello, Dr. Carlheim-Gyllenskjold, Professor Mascart, Professor T.
Mendenhall, Dr. A. Schmidt, Dr. C. A. Schott, and Professor A.
Schuster.
International Conference.
II. In consequence of a suggestion — made originally by Profes-
sor Schuster— that arrangements should be made for an Interna-
tional Conference of those interested in Terrestrial Magnetism, the
Committee decided to summon such a Conference; and the hos-
pitable invitation of the British Association, to hold the meeting
in connection with that of the Association at Bristol (September
7-14, 1898), was accepted.
The details of the arrangements are described in the President's
address. 1
Meetings of the International Conference.
IIL [For an account of meetings, see Terrestrial Magnetism,
Vol. Ill, p. 93]
1 See Terrestrial Magnetism, Vol. Ill, p. 99.
2
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i 4 o REPORT OF PERMANENT COMMITTEE, [vol. hi, no. 4 .
Meetings op the Permanent Committee.
IV. During the session of the British Association, the Commit-
tee also held meetings, on September 7th, 9th, 12th, and 13th, at
which the following resolutions were unanimously approved :
A. matters referred to thk committee by the interna-
tional METEOROLOGICAL CONFERENCE.
Four questions were referred to the Committee.
1. The first of these was the following resolution of M. Dufour
(Report of Paris Conference, p. 30) :
14 In calculating monthly means, all days are to be taken
into consideration. It is left open to each Director to give,
in addition, means calculated without taking disturbed days
into account."
This was approved by the Committee, with the substitution
of the words " It is desirable " for the words " It is left open
to each Director."
1. a. The Committee were also of opinion that the quiet days
chosen by the Directors of the different observatories should
be communicated to the President of the Permanent Magnetic
Committee, and circulated by him ; and also that it is desirable
to inquire if it will be possible to select the same quiet days
for the different observatories.
2. The second resolution referred to the Committee was the fol-
lowing, proposed by Professor von Bezold and M. Mascart
(Report, p. 31):
" It is desirable to publish the monthly means of the com-
ponents X, F, Z, and, at least for the months of January
and July, the differences dX. dV. dZ. of the hourly means
from the preceding means."
In lieu of this, the Committee adopted the following resolu-
tion:
" It is desirable to publish the monthly means of the geo-
graphical components of the magnetic force for each month,
and also the differences between the hourly means for each
month and the monthly means for that month."
3. The third resolution referred to the Committee was the follow-
ing, proposed by General Rykatchew (Report, p.32) :
44 It is desirable for the progress in Terrestrial Magnetism
that temporary observatories should be installed in certain
localities, especially in tropical countries."
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INTERNATIONAL MAGNETIC CONFERENCE. 141
On this subject, a report 1 had been prepared, at the request of
the President, by Professor von Bezold and General Ryk-
atchew.
After considering the report, the Committee resolved :
41 That it is desirable that temporary magnetic observatories
should be established in places such as the following : Tasch-
kent, Peking, the Lick Observatory, Quito, Para, Colombo,
Cape of Good Hope, St. Paul or New Amsterdam, Hono-
lulu, and Point Barrow or Sitka, or some other station in a
high latitude in North America.
" That these observatories should, if possible, be provided
with both absolute and variation instruments, of which the
latter should be self-registering instruments, and should be
established for at least seven, and, if possible, for eleven or
twelve years — i. e. t for a complete sun-spot period."
The Committee were informed by Dr. C. Schott that it was
the intention of the Coast and Geodetic Survey of the United
States to establish a magnetic observatory at Honolulu.
In the course of the discussion on the above resolution, the
Committee also resolved :
3. a. "That it is desirable to point out that observatories at
great distances from others should be provided with both
absolute and self-registering variation instruments."
4. The fourth matter referred to the Committee was the ques-
tion as to the relative advantages of long and short magnets,
raised by M. Mascart at the Paris Conference. (Report, p. 39.)
On this subject, a report 2 had been prepared, at the request of
the President, by M. Mascart.
After considering this report, the Committee resolved :
"Unless special reasons exist to the contrary, it is desirable
that the dimensions of the magnets should be as small as
possible ; provided that the accuracy of the results is ade-
quately maintained."
B. RESOLUTIONS PASSED BY THE COMMITTEE ON MATTERS ARISING
DURING THE INTERNATIONAL CONFERENCE.
5. Professor Eschenhagen made a statement to the Conference
as to his recent investigations on minute disturbances made
by very sensitive apparatus with a very open-time scale.
In view of this statement, the Committee expressed their
1 Published in Terrestrial Magnetism, Vol. Ill, p. no.
•See Terrestrial Magnetism, Vol. Ill, p. 1x4.
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142
REPORT OF PERMANENT COMMITTEE, [vol. m. No. 4.]
sense of the importance of the resolutions on this subject
passed by the Paris Conference (Report, p. 35), and the hope
that the principal observatories would carry out simultaneous
observations of the character proposed.
M. Moureaux informed the Committee that preparations for
such observations were already complete in the observatory at
Pare St. Maur.
The Committee took note of the statement that Professor Bs-
chenhagen would be willing to give information as to the con-
struction of the instruments used by him.
6. The Committee also passed the following resolution :
"The Committee is of opinion that the early establish-
ment of a magnetic observatory at the Cape of Good Hope
provided with absolute and self-registering variation instru-
ments, would be of the highest utility to the science of ter-
restrial magnetism, especially in view of the Antarctic ex-
peditions, which are about to leave Europe, and that the
observatory should be established at such a distance from
electric railways and tramways as to avoid all possibility of
disturbance from them."
Directions were given that the proper steps should be taken
to obtain the approval of the British Association for this res-
olution, with the request that, if approved, it should be for-
warded to the Colonial Government.
7. On the motion of Dr. Adolph Schmidt, the Committee resolved:
"That it is desirable that magnetic observations taken in
regions not included in a magnetic survey, should be re-
peated from time to time, care being taken to secure the
idenity of the point of observation."
8. Professor Eschenhagen was requested to draw up a de-
tailed scheme for the exchange beween the various observa-
tories of the curves of the self-registering variation instru-
ments taken during important magnetic storms; and to lay
the scheme before the next meeting of the Conference.
9. With reference to certain inquiries which Professor Eschen-
hagen suggested should be addressed to the Directors of Mag-
netic Observatories, the Committee was of opinion that,
although it would be outside the scope of their duties to make
the inquiries, it was desirable that the information should be
collected and published. 1
1 This information is being collected now by Terrestrial Magnetism, and will be
published in the Journal in the near future.— Ed.
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INTERNATIONAL MAGNETIC CONFERENCE. 143
10. After the discussion on the magnetic disturbances introduced
by electric railways and tramways the following resolution
was adopted by the Committee :
"The Committee are of opinion that any sensible mag-
netic disturbance produced in a magnetic observatory by
electric railways or tramways, is seriously detrimental,
and may be fatal to the the utility of the observatory.
They consider that special precautions should be taken
to prevent such disturbances, and append as an example
the provisions for the protection of the Kew Observatory
inserted in a bill passed by the English Parliament authoriz-
ing the construction of an electric railway, the nearest point
of which is to be at a distance of one kilometer from the ob-
servatory. (Appendix II)."
Future Organization of the Committee.
11. The Committee took into consideration their own future or-
ganization, and passed the following resolutions :
"It is desirable that Terrestrial Magnetism should con-
tinue to be within the scope of the International Meteoro-
logical Conference, provided that :
(a) " Invitations to attend that Conference are issued as widely
as possible to Directors of Magnetic Observatories and to all
students of Terrestrial Magnetism.
(b) "That the Permanent Committee on Terrestrial Magnetism
And Atmospheric Electricity, as established at the Paris
Conference, be continued.
(c) " That in future there shall be a magnetic section of the In-
ternational Meteorological Conference which shall elect, or
otherwise share in the appointment of a permanent Mag-
netic Committee.
(d) "That the Magnetic Committee have power to summon an
International Magnetic Conference at times other than
those at which the whole of the International Meteorolog-
ical (and Magnetic) Conference may meet."
The Committee also consider that the President of the Perma-
nent Magnetic Committee should only hold office between
two succesive meetings of the International Meteorological
(and Magnetic) Conference.
(Signed,) Arthur W. RCcker,
September 13, 1898. President.
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144 REPORT OF PERMANENT COMMITTEE, (vol. in. no 4 j
Appendix I.
Proceeedings at the International Magnetic Conference held at
Bristol, September 8-13, 1 898. (Already published in the Journal.)
Appendix II.
Clause for the protection of Kew Observatory.
(1) The whole circuit used for the carrying of the current to and
from the carriages in use on the railway shall consist of conductors which
are insulated along the whole of their length to the satisfaction in all re-
spects of the Commissioners of Her Majesty's Works and Public Build-
ings (in this section called " the Commissioners,") and the said insulated
conductors which convey the current to or from any of such carriages
shall not at any place be separated from each other by a distance ex-
ceeding one-hundredth part of the distance of either of the conductors
at that place from Kew Observatory.
(2) If, in the opinion of the Commissioners, there are at any time
reasonable grounds for assuming that, by reason of the insulation or
conductivity having ceased to be satisfactory, a sensible magnetic field
has been produced at the Observatory, the Commissioners shall have the
right of testing the insulation and conductivity upon giving notice to
the Company, who shall afford all necessary facilities to the engineer or
officer of the Commissioners, or other person appointed by them for the
purpose, and the Company shall forthwith take all such steps as shall in
the opinion of the Commissioners be required for preventing the produc-
tion of such field.
(3) The Company shall furnish to the Commissioners all necessary
particulars of the method of insulation proposed to be adopted, and of
the distances between the conductors which carry the current to and
from the carriages.
Appendix III.
[This consists of the following three papers which have already
been published in the Journal, viz. : President's Address, Report
of Professor von Bezold and General Rykatchew, and Professor
Mascart's Report. — Ed.]
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THE TORONTO MAGNETIC OBSERVATORY.
By R. F. StuPART, Director of the Meteorow>gicai. Service of Canada.
From an early period of the meetings of the British Association for
the Advancement of Science, the interests of Terrestrial Magnetism had
received no inconsiderable share of the attention of its members. In the
year 1834 a magnetic survey of the British Isles was commenced and
carried through in the two following years by the joint labors of five of
its members. In 1835 the Association called for a report from one of
its members, on the state and progress of researches regarding the geo-
graphical distribution of the magnetic forces on the surface of the globe;
it was proposed to ground on this preliminary examination an applica-
tion to the Government to aid in the prosecution of the inquiry in re-
mote parts of the Earth, unattainable by the means at the command of
the Association itself, or of its individual members. This report, pre-
sented in 1837, was taken into consideration at the meeting of the Asso-
ciation at Newcastle in 1838, and a memorial was addressed to the Gov-
ernment, which, being favorably received by Her Majesty's Ministers,
originated the naval expedition equipped in the following year for the
magnetic survey of the high latitudes of the Southern Hemisphere.
Deeming the opportunity a fitting one, the British Association availed
itself of the same occasion to solicit the attention of Her Majesty's Gov-
ernment to the expediency of extending the researches to be accom-
plished by fixed observatories to certain stations of pre-eminent mag-
netic interest within the limits of the British Colonial dominions. The
stations named were Canada and Van Diemen's Island, as approximate
to the points of the greatest intensity of the magnetic force in the
Northern and Southern Hemispheres; St. Helena, as approximate to the
point of least intensity on the globe, and the Cape of Good Hope as a
station where the secular changes of the magnetic elements presented
features of peculiar interest.
The Committee recommended that the proposed establishments
should be placed under the general supervision of the Ordnance Depart-
ment of the Army. The Government having expressed a desire that
such extensive arrangements involving a considerable expenditure
should be strengthened by the concurrent support of the Royal Society,
a deputation was appointed to express the cordial participation of that
Society in the recommendation both of the naval expedition and of the
fixed observatories. Arrangements having been completed, Lieutenant
Charles James Buchanan Riddell, R. A., was selected for duty in Can-
ada. Leaving his detachment, consisting of four non-commissioned
officers of the artillery, to embark with the instruments on a vessel
bound direct to Quebec, he proceeded himself to Canada by the more
145
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I4 6 JR. F. STUPART. ivol. hi, no. 4O
expeditious route of the United States. Having waited on the Governor-
General of Montreal to present a letter of introduction with which he
had been furnished by the Master-General of Ordnance, and having com-
municated with the commanding engineer, to whom he was the bearer
of instructions and authority to build an Observatory, he proceeded to
examine different localities which were suggested as convenient sites.
The preference was finally given to Toronto, where a grant of two and
a half acres of land belonging to the University of King's College was
offered by the council of the University. The first Observatory build-
ing was of logs, rough-cast on the outside and plastered on the inside ;
it was completed during the summer of 1840, and the observations were
begun in September. The operations of the Observatory as an Imperial
establishment were brought to a close in the early part of the year
1853, and were resumed under the authority of the Provincial Govern-
ment in July of the same year.
In the autumn of 1853 the present Observatory was commenced, to
take the place of the old building. Very great care was taken during
construction to insure entire freedom from magnetism in all the stone
used, and all nails and fastenings were of either copper or zinc.
For twenty-three years the position of the Observatory was as far as
known, faultless ; observations were carried on systematically and care-
fully, and results were given to the scientific world, which, with those
obtained under the old military regime have made the Toronto Observa-
tory famous in the history of Terrestrial Magnetism.
In 1876, however, trouble began with the erection of a large brick
building close to the Observatory, causing some very small changes in
zero values. Then followed a few years later electric light circuits
which produced a change in the force instruments whenever the cur-
rents were turned on or off; this difficulty was in part overcome by the
Light Company courteously agreeing to arrange their wires in the vi-
cinity of the Observatory in such a manner that currents would coun-
teract each other. The next difficulty occurred when a large addition
was made to the neighboring building before mentioned, tons of iron
being used in construction in all too close proximity to the mag-
netic instruments, and much time and labor have been required to de-
termine the precise effect of this "iron mine" on the various instru-
ments. It was not, however, until the autumn of 1892, when the trolleys
began to run, that we began to suspect that sooner or later the Mag-
netic Observatory would have to be removed to another site.
The magnetic instruments in the Observatory consisted of those
brought out by Lieutenant Riddell, in 1840, of which eye-readings have
been taken six times each day, and of another set of instruments, con-
sisting of a bi filar for the measurement of the horizontal component, a
balance needle for the vertical force, and a declinometer, all of which re-
cord photographically.
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TORONTO MAGNETIC OBSERVATORY.
147
.LAI****
Electric cars first ran in Toronto, on August 17, 1892. The line first
put in operation was that on Church Street, which was followed on Sep-
tember 5th, by one on King Street, between George and Dufferin Streets.
During the first few. weeks, while a very small vibration of the needle was
discernible on the V. F. curve, it was generally almost inappreciable,
and it was not until September 20th that the movement increased to an
extent sufficient to really impair the value of our magnetic curves. A
marked increase of current must have been used on that day and after-
wards. On October 10th the cars first ran on Yonge Street, and there
was only a very small increase in the vibration, but a decrease of about
.000070 of a dyne was observed when the current was on.
About 10 A. M., January 14th, there was a marked increase of vibra- ^ moX aM o
tion, and the vertical force increased about .000200 one dyne. This dis- «>■""!:
turbed period was only temporary, and shortly after 5 P. M., on the 17th,
there was a reversion to the smaller vibrations. These continued until
May 15th, when larger vibrations began again, and continued, with vary-
ing intensity during the summer, while the decrease of the V. F. with
the current ranged from about .000200 to .000500. This disturbance was
very great between September 12th and October 17th, and at intervals
during the following year; but there was no radical change in conditions
until December 17th, 1894, when a decrease of V. F., while the current was
on, was changed to an increase, this occurring when the cars first ran on
McCaul Street. Throughout 1895 the vibration and amount of perma-
nent deflection was very nearly as it has been since; but on October 15th
the increase of V. F. with the current was again changed to a decrease,
this occurring at the time that the railway company made certain changes
in the feed wires. It is noticeable that, although several changes oc-
curred in the V. F., it at times having been less with the current on and
at other times greater, the horizontal force showed a decrease on all oc-
casions with the turn on of the current. This decrease during the past
two years has been .000200 to .000500 of a dyne. No appreciable deflec-
tion of the declinometer magnet can be noted, the only effect being a
continuous vibration, which has rendered the curves very ragged and
difficult to read with accuracy.
A study of the traces during the times that the various electric lines
were put in operation, showed that, with the currents ordinarily used,
there was little effect at three-quarters of a mile, and a further survey
with a portable instrument afforded further evidence in the same di-
rection.
Before definitely recommending that the Magnetic Observatory should
be removed from Toronto, the Director wrote to various well-known mag-
neticians, present at the meeting of the British Association in August,
1897, requesting the favor of their presence at the Observatory to inspect
the photographic magnetic curves there obtained, with the view of ex-
pressing an opinion as to the advisability of continuing the records at
3
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148 A\ F &TUPART. [vol. in, no. 4 ]
the present site, or of removal to some point distant from electric tram-
ways. Professor Ru'cker, F. R. S., Professor Carey Foster, F. R. S., Pro-
fessor FitzGerald, F. R. S., Dr. van Rijckevorsel, and Professor Frank
Bigelow were the gentlemen who courteously accepted the invitation, and
were pleased to sign a statement that, in their opinion, the value of the
magnetic observations at Toronto had been seriously impaired by the
trolley system, and advised removal to some other site.
It then having been decided to remove the Observatory, a point was
chosen nine miles northeast of the former Magnetic Observatory, lati-
tude 43 47' N., longitude 79° 16' W., easily accessible by railway, and yet
very unlikely to be invaded by the trolley system. At present there is
no electric railway within seven miles, and little prospect of one within
five miles for many years.
The new Observatory, which was commenced in June and finished
during the early days of September, consists of two parts — a circular
stone cellar, and a superstructure. The cellar is nineteen feet in diam-
eter, the walls two feet in thickness, the floor concrete, and the roof cov-
ered with felt and gravel, in which, on stone piers sunk in concrete to
depth of six feet below the floor, are placed the self-recording photo-
graphic instruments; namely, the declinometer for recording changes in
the direction of the magnetic needle, and the bifilar and vertical force
instruments for registering, respectively, changes in the horizontal and
vertical components of the earth's magnetism. Above ground, and con-
nected with the cellar by a flight of steps, is an erection which is di-
vided into two portions, in the larger of which absolute magnetic de-
terminations will be made, piers being provided on which to place the
necessary instruments, and an adjustable opening on the roof for transit
work ; the smaller portion is an office, which will be heated by a copper
stove.
Observations were first made in the new Observatory on September
10th, and by October 1st all the instruments had been adjusted in their
new position, and everything was running smoothly. Results already
obtained show that values will differ but slightly from those obtained at
the old Observatory, and a very careful comparison was made before dis-
mounting the old eye-reading instruments in Toronto.
Very great care has been taken in selecting materials for the build-
ing. Every stone used was tested for magnetic effect, and none but cop-
per or zinc nails and fastenings have been used.
There appears to be every prospect that the new Observatory will be
admirably suited for the purpose for which it was designed, and there is
strong reason to think that the series of observations at Agincourt will
be practically a continuation of the old and valuable series of observa-
tions made in Toronto. All the photographic records will be sent for
development to the Toronto Observatory, which continues to be the
Central Office of the Meteorological Service of Canada.
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THE ALTITUDE OF THE AURORA ABOVE THE
EARTH'S SURFACE.
By Professor Cleveland Abbe.
(Concluded.)
Jesse.— O. Jesse has computed the altitude of an auroral arch
observed throughout Europe in the evening of October 2, 1882. 1
He combines the observations made at nine stations by the method
of least squares, and deduces as his result an auroral arch ver-
tically above the magnetic parallel, that is 67.55 degrees distant
from the magnetic pole, and whose altitude above sea-level is uni-
formly 122.2 kilometers, with a probable error of 4.5 kilometers.
The assumptions that underlie Jesse's calculations seem to be as
follows : (1) That there was but one continuous arch of light from
England to Buda-Pesth. (2) That it was at the same uniform height
above sea-level. (3) That it was vertically above some one mag-
netic parallel on the earth's surface ; that is to say, a horizontal
curve perpendicular to the local magnetic meridians, and, in Eu-
rope, agreeing so nearly with the curve of equal magnetic dip and
the curve of equal magnetic intensity that it was not worth while
to attempt to distinguish between them. (4) That the plane of each
local magnetic meridian passes through the earth's center. (5) As
the arch appeared to each observer to change its zenith distance by an
appreciable amount in the course of time, and as Jesse used, when
possible, the extreme southern position, the implied assumption is
that the southern position was simultaneously attained at the same
height and at the same time for all stations. (6) The assumed par-
allelism between the auroral arch and the magnetic parallel should
evidently refer to the temporary disturbed magnetic condition that
prevails during an aurora; but the calculation assumes that this
agrees with the normal magnetic condition as shown on the mag-
netic chart published in the "Annalen der Hydrographie " for 1880.
(7) As in most other calculations of this kind, Jesse assumes that
the magnetic parallels at the altitude of the aurora agree with those
at the earth's surface.
This was a bright, well-defined arch, observed between 7.15 and
8.30 P. M., Berlin time, 1882, October 2d. In general, it lay along a
1 Jesse: Die Hohe und die Lage des Nordlichtbogens vom 2 October, 1882.
Astronomische Nachrichten. No. 2496, March, 1883 Vol. CIV, pp. 369-378.
149
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Longitude
—Zenith Distance of Arch-
Latitude
[From Greenwich]
Observed
Computed
5I°73 N.
i°93 w:
-So°-6o
-63°-3
52.37
1 .26 w.
-76
—67.8
51 22
.27 E.
-48
—47.1
49.02
1 .15 E.
+41
4-46.1
53-22
6.56 E.
—61
— 61 .9
52 41
13-30 E.
— 15
—15 5
52 .74
15 .22 E.
—17
—17.0
51 II
17.04 E.
+56
+53-6
47 -5o
19 .05 E.
+80
4-80.8
1 50 CLE VELASD ABBE. 1 voi~ 111. No. 4-]
magnetic parallel. Nine stations observed the altitude of the arch at
its intersection with the magnetic meridian, as follows:
Station
Boston
Rugby
Tunbridge
Evreux
Groningen
Steglitz
Landsberg
Breslau
Buda-Pesth
Note. — The Zenith Distance of the Arch is given in the fourth column
where minus indicates that it passed south of the zenith. The zenith dis
tance, as computed under the assumptions and conclusions arrived at by
Jesse are given in the fifth column.
The agreement of the observed and calculated zenith distances
over this whole region of 1,200 miles in longitude is so close
as to strike the attention very forcibly, but a careful study of the
numerous assumptions or hypotheses on which the calculation is
based will show that these mutually compensate each other's er-
rors. It would be possible to devise another set of six or eight
hypotheses that would give equally close agreement in observation
and computation. In lact, those adopted by Jesse, while they
seem to hold good for all stations east of Greenwich, are decidedly
discrepant for the two stations to the westward.
In this region of the earth the curves of equal magnetic dip
and equal magnetic intensity, agree closely with the magnetic par-
allel — namely, the curve perpendicular to the magnetic meridians —
so that a comparison of the auroral arch with each of these could
lead to no decision as to whether it followed one rather than the
other; therefore, the magnetic parallel was retained as the basis of
the computation, assuming that the auroral arch is parallel to it.
The further assumption that the magnetic meridian passes through
the earth's center seems wholly inadmissible from a magnetic point
of view, even when we deal with the average or normal magnetic
condition, and greater departures must be expected in times of
great magnetic disturbance, such as prevail during auroras.
Von Bobrik. — The auroral observations at the international
polar station occupied by the Austrian expedition, 1882-3, at J an
Mayen (N. 71 ° o'; W. 8° 28'), were published with the accompany-
ing memoir by Von Bobrik, after the death of Weyprecht. In his
chapter on the altitude of the aurora above the earth's surface he
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THE ALTITUDE OF THE AURORA. 151
computes the altitude of certain observed arches by the Norden-
skold method, assuming the auroral pole to be 18 12' distant from
Jan Mayen Island, and obtains the following results, expressed as
decimals of the radius of the earth, and which I have approxi-
mately converted into English miles:
Radii
Miles
O.IO5
420
O.OI3
52
O.O30
I20
O.OI8
72
O.234
93 6
O.O42
168
O.183
732
But eventually he relinquishes this method, with the conviction
that the computations give us nothing satisfactory. He finds Galle's
method not applicable to high latitudes.
On page 206 he quotes a case of an auroral ray that was cer-
tainly seen within a few feet of the observer, and states that at Jan
Mayen the layers of haze may be generally classified as:
The highest, on a level with the high cirrus;
The middle, at altitudes of 800 or 1,000 meters;
The lowest, at altitudes of 150 to 250 meters.
There is every indication that the auroral light occurs between
the medium and the highest layers of haze, ordinarily.
As the sunlight may illuminate the highest haze, he shows by
computations that the aurora is often visible when the sunlight il-
luminates the upper stratum of air, but in such a way that it can not
be mistaken for the aurora, and that the latter must emanate from
a lower stratum.
He indorses the general conclusion given by Weyprecht : " From
all this we derive the conviction that the altitudes of the auroras
vary within considerable limits, and we must not conclude that the
results are contradictory when the absolute measurements — which
are, of course, subject to error — give very discrepant figures."
On page 208 we find that intimate connection with the clouds
is fully warranted by the following items: (1) Clear air; (2) needles
of snow occur when the corona breaks up in a clear sky; (3) clouds
change from one form to another in connection with the aurora;
(4) the aurora and the clouds have a common direction of motion ;
(5) the aurora occurs on the edges of clouds; (6) the illumination
of the clouds, perfectly similar to that of heat lightning, occurs with
every large aurora ; (7) a change, and usually an increase, of wind
follows the aurora.
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*52
CLE V ELAND ABBE. [Vol. hi. no. 4 J
Gyixbnskoi<d. — The parallax method was tried in 1882-3 by the
Swedish observers at Cape Thordsen, Spitsbergen. See the report
by Carlheim-Gyllenskold. They used a base line only 573 meters
long but it was inclined 18 38' to the horizon, the upper end be-
ing on anemometer hill 183 meters above the lower end; the hori-
zontal projection of this base line was, therefore, 542.6 meters. At
each end Mohn's aurora and cloud theodolite was used, and the ob-
s rvers were in constant telephonic connection with each other.
The details of the parallax observations are given on pages 176,
177, of Volume II, of the Swedish Polar Expedition, but the details
of the calculations by Bravais's method and the amplitudes of the
arches are given on pages 61-65. Gyllenskold recognizes the fact
that the auroral arches do not have their center at the auroral pole
any more than they have at the terrestrial pole. On calculating
the radius of curvature of the magnetic parallels passing through
Spitzbergen, he finds that it is about 6o° o' of a great circle which
agrees so closely with 58 31', the radius of curvature of the au-
roral arches deduced from observations of amplitude, that this
coincidence might seem an argument in favor of the hypothesis
that the arches are parallel to the magnetic parallels, and there-
fore belong to arcs that have their centers at the magnetic pole.
Galle's method. From the observed position of the center of
the corona, the altitude of the auroral beams may be calculated by
adopting the hypothesis of Galle, which is to the effect that the
beams of light are parallel to the free magnetic needle at the sur-
face of the earth. [This hypothesis had been shown to be inac-
curate, both by myself (Report C. S. O., 1876), and by Ekama
(Zeitschrift, Ost. Ges. Met. XX, p. 67-69).] Eighty-seven observa-
tions of the corona are given in detail in Vol. II of the Swedish
Polar Expedition, but no attempt is made to compute the altitude
by any modification of Galle's method.
Bravais's method by the breadth of the arch. Data for comput-
ing altitudes by this method for forty-seven arches are given in
the Swedish volume, and it is concluded that the most probable
value of the altitude of the lower edge of the auroral arch is 264
kilometers, and that of the upper edge, 372 kilometers.
Zones. When a zone or band of light passes through the zenith,
forming a geometrical zone on a sphere whose center coincides with
that of the earth, the zone is broadest near the zenith and nar-
rows as it approaches the horizon to the east and west. These
zones are often traversed] by longitudinal striae. The height of
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THE ALTITUDE OE THE AURORA.
*53
such a zone was calculated by Tromholt, who obtained 146.95 kilo,
meters from nineteen observations. (See page 79 of the Swedish
volume.)
Parallax. For the purpose of parallactic observations two
stations were occupied, as before mentioned; namely, Cape
Thordsen and anemometer hill. Thirty-two simultaneous obser-
vations at opposite ends of this short base would have given a
positive parallax if the auroral arches had been discrete beams
at low altitudes, but the actual results were as follows (see p.
176-79):
1882, Dec. 11
1883, March 3
4-2° 30'
+o°
30'
—2 50
—
09
—
°5
— o° io'
—
06
1883, Jan. 14
—
47
— o°5</
—
27
-fo 35
—0
12
4-0 20
—
40
— 20
—
22
—0 30
—
17
—0 25
—
17
-|-o 20
+4
4i
— 1 00
+0
03
—0 05
—0
3
40 40
—0
— 10
—
16
+0
23
— o°o8 /
+0
16
1883, Feb. 3
—0
19
+ i°o 5 /
+5 4o
— o°n'
+1 55
1883, March 8
—0 05
—i°
oc/
-6 35
4-o
01
+ 1 05
—8
55
-fo 10
4-2
29
4-2 00
These may be summarized as in table below. I have made
several different computations for the same date, in order to show
the effect of rejecting one or more largely discrepant values :
Parallaxes Extremes
Date Neg. Pos. Neg. Pos. Mean
I>ec. 11 11 2°so / 2° y/ -o° 10'
Jan. 14 74 1 o o 35 —08
Feb. 3 26 6 35 5 40 -to 40
16 o 5 5 40 4-1 42
Mar. 3 10 2 o 47 4 41 4-0 11
44 91 o 47 o 30 — o 24
43 0580 23 —08
" 13 4 o 58 o 30 — o 11
Mar. 8 22 8 55 2 29 — 1 51
44 21 1 o 2 29 4-0 30
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I5 4 CLEVELAND ABBE. [vol. hi, no. 4 O
It will be noticed that the number of positive and negative
parallaxes is about 18 and 26 respectively; or after rejecting some,
as is done by Carlheim-Gyllenskold, 17 and 23, respectively, which
is evidently sufficient to show that there has been no true deter-
mination of parallax in any case. But as the general result
adopted by that author has been quoted as having some weight,
the following translation of a paragraph on page 178 will show
how the calculus of probabilities was forced to give a plausible
altitude from these figures: "I divide the total number of paral-
laxes into two groups, according as the angular altitude of the arch
was less or greater than 45 . Thirty-two observations on arcs,
whose altitude was between o° and 37 , give me a mean altitude
of 14 19' and a mean parallax of — 2.7^4.2'. Six observations on
arches having altitudes between 64 ° and 79 ° give me mean altitude
of 76 10', and a mean parallax of -ri° 43'±:6.7'. Within these
limits of probable errors, and giving to these two parallaxes the
values which accord best among themselves — namely, 4-1.5'= — 2.7'
2.7'+ 4.2' and i° 36'=i°43' — 6.7' — we find for the arches near the
horizon an elevation of at least 81.90 kilometers, and for the arches
lying near the zeqith an elevation of 19.83 kilometers or more.
These parallaxes, therefore, give to the aurora borealis a mean alti-
tude of 72.2 kilm., if we take account of the different weights of the
observations; that is to say, the weights of these two mean altitudes
are supposed to be proportional to the number of observations."
Fearnley, as quoted by Carlheim-Gyllenskold, Swedish North
Polar Expedition, Vol. II, p. 62, assumes that the auroral arch has
the same curvature as the observed magnetic parallels at the earth's
surface, whence by this modification of Bravais's method he finds
from sixteen observations at Christiania a mean altitude of the
lower edge of the arc 175.6 kilometers.
Nordenskold, as quoted on the same page, assumes that the
arch forms a small circle on the terrestrial sphere, having its center
at the pole of the northern auroral belt, or 81 ° N. and 8o° W., but
as this hypothesis is not well verified, Carlheim-Gyllenskold has
repeated the calculation and finds a mean altitude of 34 kilm. for
the observations used by Nordenskold.
Bergman has calculated the altitudes for ten auroras in the seven-
teenth century. He made use of arches whose summits were situ-
ated in the astronomical meridian, and whose centers were assumed
by him to be at the north pole of the earth. This erroneous suppo-
sition gave him a mean altitude of 685 kilometers.
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THE ALTITUDE OF THE AURORA.
155
Ekama calculated the altitudes of nineteen arches observed at
the Sea of Kasa, using Nordenskold's assumption, and obtained
the mean altitude of 212.8 kilometers.
Steen. — At the Norwegian polar station, Bossekop, in Alten
(see the " Beobachtungs-Ergebnisse," 2te Theil, Christiania, 1888),
Steen says that the forms under which the auroras appeared in
1882-83, agreed completely with those pictured by Lottin and
Bravais for 1838-39. The results of the Norwegian observations
give no detailed drawings, because during the whole time not a
single form of aurora was observed which was not published in
the work of the French observers ("Voyages en Scandinavie").
No attempt at computations of altitudes is given in this volume ; as
before stated the data were submitted to Tromholt, who occupied
the station at Koutokeino, 130 miles south of Bossekop, for the
purpose of making simultaneous comparative observations, and
the results of his computations are given in the present summary
of his report. On the other hand, the Norwegian observations, as
printed in full by Steen, record many cases in which bands, arches,
beams, or other forms of auroral light were observed close down to
the apparent horizon ; as the absorption of light by the atmosphere
would, in this case, entirely obscure, any auroral glow that ema-
nated from very distant points, it follows that in such cases the
light must have originated near the ground and not far from the
observer.
Andree. — Quoting the Swedish observations at Cape Thord-
sen, 1882-3, Spitzbergen, Andr6e (see Tome II, section 2) states
that the observations of atmospheric electricity (page 21) do
not indicate — as Dellman had deduced from his observations
of October 1, 1859 — that the tension is at all increased during
the aurora borealis; on the contrary, it is at that time sensi-
bly diminished. This is also proved by the fact that on one
occasion, December 1, 1882, at oh. 50m. negative electricity
was observed in a perfectly clear sky, followed, at the end
of a few minutes, by an aurora borealis. This diminution is
often so considerable and so sudden (see March 6th and February
7th) that it is perfectly comparable with the negative perturbations
during bad weather and the precipitation of atmospheric moisture.
This conformity between the changes of atmospheric electricity
and phenomena, apparently so diverse, is not confined merely to a
temporary diminution of intensity. It shows itself also in the cir-
cumstance that a short time before the intensity falls it increases
4
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156 CLEVELAND ABBE. [Vol. hi, no. 4 -l
appreciably in the positive direction, and when the phenomenon
has ceased it returns to a relatively high value. This circumstance
of the appearance of an aurora borealis in a perfectly clear sky
affords an analogy with those phenomena of atmospheric electric-
ity which preferably occur during, and really have some relation to
the formation of clouds and the precipitation of moisture, and is re-
markable in every respect. Perhaps an explanation is found in
the fact, demonstrated by Meissner, that the condensation of aque-
ous vapor does not cease, but that it does become invisible when
the pressure of the air falls below a certain limit. We can, then,
suppose that the condensation of aqueous vapor, when it goes on
at a great height above the earth, although itself invisible, pro-
vokes or favors electric phenomena analogous to those that are
produced, under similar circumstances, at the surface of the earth.
Paulsen. — Observations Internationales Polaires. Expedition
Danoise. Obs. de Godthaab. (Greenland.) Tome II. 20-33.
Auroras at Nennortalik, by Garde, November, 1883 — April, 1885,
page 17-19:
" The arch and the ribbon types are not separated from each
other in the summary because these two forms very frequently pass
from one into the other. These forms together constitute the most
frequent type ; the auroras generally begin in the evening by show-
ing one or both of these forms, at an altitude of 35 or 40 degrees
above the horizon in the north-northwest. The longitudinal direc-
tion of these ribbons generally trends from east-northeast to west-
southwest; the intensity is rather feeble. In proportion as the
evening progresses the intensity augments, and the evolution of
the aurora borealis brings out draperies, bundles of rays, and in
some cases coronae, while at the same time the whole phenome-
non approaches the zenith, and afterwards extends over to the
southern part of the sky. New ribbons appear in the northern
part of the sky, and the same phases repeat themselves until the
morning dawns; then we see the entire heavens either covered
with feeble rays, elongated, pointing toward the zenith, or with ill-
defined lights. The phenomenon is thus often terminated by an
expiring light, the summit of whose arch is about 20 above the
south-southeast, and which seems to be the limit of a dark seg-
ment." 71 per cent of aurorae move from N. to S., 19 per cent
from S. to N., 8 per cent from W. to E., and 2 per cent from
E. to W., by measurements with theodolites, having a base line of
I247.8_meters lying in the magnetic meridian, and using luminous
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THE ALTITUDE OF THE AURORA. 157
signals so as to obtain absolute simultaneity and measuring only
points of the auroral arches that lie in the magnetic meridian,
Lieutenants Garde and Eberlin obtained the following results :
1884, February 10th, parallaxes 2°.7, 3°.i, 5°.8, o°.8, 3°.8, 4°.5,
o°.9, whence the calculated altitudes in kilometers for those cases
in which the parallax exceeded i° were: 7.3, 15.3, 5.4, blank,
7.7, 1.8, blank.
1884, February nth. Parallaxes, 5°.9, i°.8, 3°4, 2°.8, 2°45,
i°.6, i°. 5 , 2°.2, i°. 5 , i°. 5 , i°. 3 , 2°.6.
Among these twelve observations were many that referred to
the same arch, and ought to have given the same altitudes, and yet
the results expressed in kilometers were sufficiently discrepant, viz. :
1.6, 5.7, 4.4, 3.0, 4.3, 5.6, 5.8, 6.0, 7.4, 8.3, 12.9, 7.8.
During the thirty-five minutes occupied by these observations
the altitude above the north horizon increased somewhat, and the
actual altitude appears to have increased as steadily and as decid-
edly as the apparent. Observations ceased because the arch be-
came indistinct.
Paulsen gives, on pages 20-33, tne results of his own observa-
tions near Godthaab. His stations at Godthaab were on opposite
sides of the fiord in the same magnetic meridian, and distant 5.8004
kilometers. The observations were made always on the lower edge,
which was always the sharpest edge of the arches, and were con-
fined to the common vertical plane. Simultaneity was secured by
signals. The resulting parallaxes and altitudes were :
1882, October 17th, parallax, o°45, io°.2, 4°.6, 6°.4, o°.2, o°-5,
7°.5>o°.o, i°. 5 , i 4 2 . 4 , 85°.9-
Altitudes in kilometers, blank, 2.0, 45.1, 47.0, blank, blank, 3.7,
blank, o.6, 1.4.
" The two last auroral observations lay close to the fiord between
the two stations, and consisted of curtains formed by rays which
were joined to each other at their lower extremities. The first
curtain unfolded itself after more than half an hour of waiting.
There was then only one aurora between the two stations. The
curtain continued only a short time, and disappeared by fading
away. The second curtain presented similar phases in its forma-
tion and disappearance. These auroral curtains did not resemble
ordinary curtains, with undulating folds. They belonged to the au-
roral type that Kleinschmidt has called "rangees de rayons station-
naires," or rows of stationary rays, which are presented under the
forms of rays in alignment, joined together at the base, and quite
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1 58 CLE VELAND ABBE. [Vol. hi, No. 4]
stable, their intensity increasing steadily from below upwards. Both
of these forms of auroras advanced from the interior of the fiord, and
the movement propagated itself longitudinally by new formations
in the direction of the length on the side turned toward the sea.
Before the formation of the rays a light of feeble intensity arose, in
the midst of which, little by little, there were produced many lumi-
nous "nervures," viz., sinuous lines. In this manner we assisted
at the birth of the phenomenon. The disappearance was analo-
gous to the formation.
The following evening, 1882, October 18th, the measurements
were: Parallax, i°.5, 6°.o, i4°.o, o°.2. Altitudes in kilometers,
59-6, 9-8, 5-3> blank.
1882, December 18th, the measurements were: Parallax, i°.2,
o°.o, 2 °.6, i6°.8, 7°. 5 , i°. 5 , 3 °.o, o°.i, 7 °.i, i°. 4 , o°. 3 , o°.o, 3 °.o,
i5°.o, 7°.o, 6°.o.
Altitudes in kilometers, 54.7, blank, 38.1, 19.2, 29.8, 7.7,67.8,
blank, 7.4, 6.2, blank, blank, 9.4, 2.0, 3.2, 2.9.
"Both at Godthaab and Nennortalik the altitudes of the arches
have only been measured when their edges were sufficiently sharp,
and the apparent motion sufficiently slow. Under such circum-
stances the measurements were made with the precision of about a
quarter of a degree. This is shown by the fact that a greater un-
certainty than this would have introduced a negative parallax in
the cases where the lines of sight were almost parallel.
"As concerns] the small altitude at which the auroras seem to
occur in Southern Greenland, I ought to say that the aurora has
been seen below the clouds both by myself and bv two of the ob-
servers of this expedition, and Mr. Kleinschmidt, who is very
familiar with auroral details, has also observed the same phenome-
non. Many times the observers have established the occurrence
of phosphorescent vapors, and fogs resembling the aurora which
displayed themselves in the lower layers below the summits of the
surrounding mountains. Thus in the journal for 1882, August
21st, "at 1.45 A. M., there appeared in the northeast a pale-green
light behind the summits of the neighboring hills ; it was at a very
slight altitude ; for the summit of the neighboring mountain, Selle,
: altitude is about 1,500 meters, was clearly seen above the
ous surface, which resembled a sheet of water illuminated by
oon. This*light rapidly disappeared. At 2.45 A. M., there
red to the south another light, which resembled the dawn of
it soon contracted into a long feebly luminous cloud, which
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THE ALTITUDE OF THE AURORA.
159
moved slowly beneath the summits of two mountains to the south-
east of us whose heights were respectively 1,200 and 900 meters,
and whose summits were distinctly seen above the luminous
cloud."
A number of descriptions of auroral light of this character are
given by Paulsen, as observed by the Danish observers at Godt-
haab, Greenland, and he adds that at the end of the summer of
1885, Captain Jansen and Dr. Hansen, of the Danish navy, ob-
served in the interior of the fiord of Godthaab an auroral drapery,
or curtain aurora, between themselves and neighboring mountains,
whose altitude was, therefore, quite small. He quotes Nordens-
kold's observation of 1883, August 25th, to the same effect.
Paulsen also gives observations and measurements to show the
speed of motion of the auroral arc in the direction of the magnetic
meridian. These speeds are as large as from three to five kilometers
per minute, or forty to fifty meters per second, corresponding, as he
mentions, to the velocity of the wind during a hurricane.
On November 18, 1882, at 2 A. M. (see page 28), lieutenant Ryder
observed six draperies pass over the. zenith within fifteen minutes,
and apparently very close to the ground ; when the last drapery
was passing the zenith, the first had disappeared in the northern
horizon.
Tromholt (see page 29), by using a base of 107 kilometers, from
Bossekop to Kautokeino, deduces altitudes of from 76 to 163 kilo-
meters, averaging 113 kilometers. But such a long base renders it
impossible to measure the altitude of the lower auroras, so that his
figures could only relate to the highest features. In order to be
assured of the identity of the points upon which the measurements *
are made, one is forced to consider only the prominent strongly
marked larger features of the aurora, such as we might assume
would be quite high up in the atmosphere if we were in southern
latitudes.
On pages 33-39, Dr. Holm gives the auroral observations at
Angmagsalik, but attempts no determinations of altitude.
In general, Paulsen concludes : " There is a certain zone that
traverses southern Greenland, having a breadth of at least four
degrees of latitude, within which the influence that produces the
aurora borealis extends from the higher regions of the atmosphere
down to the surface of the soil." After discussing the observations
of the Swedish observers at Spitzbergen, and omitting the paral-
laxes less than one degree, Paulsen concludes that these measures
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160 CLEVELAND ABBE. lvol. hi, no. 4.)
give the same result as that of the Danish observers at Godthaab,
namely: "That in the zone of greatest frequency and variety of
forms of the aurora, this phenomenon is produced generally at any
height whatever above the surface of the soil."
Tromholt. — Sophus Tromholt, of Rostock, Norway, compiled
two extensive works on the aurora, which are as yet unpublished,
but a summary of which he has published in three memoirs in
Petermanris Mittheilungen for 1892, XXXVIII, pp. 201, 236, 259.
The first of these contains a discussion of the observations made
by himself during the year 1882-83, at Koutokeino, in Finmark,
Sweden, latitude 69 o' N.; 23 3' E., in concert with those made at
the Norwegian polar station, Bossekop, lat. 69 57'; long. 23 15' E.
Bossekop was, therefore, north four degrees east from Koutokeino,
and distant one hundred and seven kilometers, or about 66.5
miles. The observations were made simultaneously at 5.15 and
6.15 P. M., Gottingen time. Besides a vast number of other details,
Trombolt states that 634 measurements were made by himself in
the azimuth of Bossekop, while at the latter place 367 measure-
ments were made in the azimuth of Koutokeino. But of these,
only sixty measurements corresponded as to time, and can be as-
sumed to refer to identical objects. He says : "It is well known
that there are still some who believe that the auroral phenomena
are, like those of the rainbow, subjective rather than objective. I
will not discuss this matter, but may express the opinion that but
few objections can be raised against the propriety of using the
present measurements for the determination of altitudes. The
method adopted can, under some circumstances, lead to erroneous
results when the horizontal extent of the arches is considerable in a
north-south direction ; but this difficulty does not come into consid-
eration when, as in the present case, both measurements are exe-
cuted on the same side of the arch. More important objections
can be raised on account of the inevitable errors of observation
which arise principally from the feebleness of the light, the indefinite
boundary, and the movement of the object itself, to which we must
add the absence of absolute synchronism in the measurements. The
measurements made by myself may, in most cases, be uncertain by
plus or minus five minutes of arc. We have further to consider that
most of the correspondent measures relate to arches at a small angular
altitude, in which case the influence of the error of observation is
very appreciable. Since most of the altitudes are small, I have, in
spite of the uncertainty of measurement, thought it proper to cor-
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THE ALTITUDE OF THE AURORA. r 6i
rect them for the astronomical refraction, using the temperatures
given by the observatious at Bossekop. ... If out of the sixty
cases submitted to calculation we consider only the forty-two that
appear to be most reliable, and that relate to the lower edge of the
arch, we find the individual altitude, as computed, lie between the
extreme limits, 19. i and 216.8 kilometers, with an average of
1 14.6.
"On the assumption that the horizontal extension of an arch in
the north-south direction is small, so that, therefore, the width of
the arch depends only upon the extent in altitude of the luminous
layer, and assuming that the direction of the layer is parallel to that
of the dipping-needle, we may compute the extent in altitude when
we know the altitude of the lower point of the lower edge of the
arc, and the width, or angular altitude of the upper edge of the
arc. If, however, the arch has a considerable thickness, then this
will enter as a factor into the observed width of the arch ; it will
increase the width that would otherwise depend only on the extent
in altitude, and so much the more in proportion as the arch is lo-
cated higher above the horizon. Now, in general, the thickness of
the arch is to be considered as a quantity that is not to be neg-
lected; but notwithstanding this, we shall in this way obtain at
least a maximum value for the extent in altitude. I have not ex-
tended this computation to special observed cases, but have tried
to ascertain to what results we should be led by using the mean
values of the angular altitudes and the breadths of the arches when
we assume that the linear altitude of the lower edge of the arch is
the above-found mean value, 114.6 kilometers." Assuming the dip
to be 76 degrees, Tromholt obtains values for the vertical extent
of the luminous sheet above the lower edge of the arch, varying
between 54 and 154 kilometers, and averaging 65.2.
In so far as Tromholt restricts himself to the parallactic method
of computing the altitudes of the arches by the use of observations
at Bossekop and Koutokeino sixty-six miles away, he is, as he him-
self clearly recognizes, at the mercy of the assumptions that under-
lie all such work, viz. : (1) That there are one or more concrete ob-
jects to be observed, each having its definite locus ; (2) that the re-
spective observers see the same object ; (3) that the object is mov-
ing so slowly that a small error in time has no important injurious
influence on the result. The true test as to whether these condi-
tions, essential to success in paralactic work, have been fulfilled, is
to be found in the internal evidence afforded by the parallaxes
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^2 CLEVELAND ABBE. [Vol. hi, no. 4 )
and the altitudes themselves. If the parallaxes vary according to
the laws of chance between plus and minus 180 degrees, that of
itself is abundant evidence that the underlying assumptions are
probably none of them fulfilled. If a majority of the parallaxes
are positive, but a considerable number negative, that is sufficient
to throw a great doubt upon the verity of some one or more of the
assumptions. If the parallaxes are all positive, but vary between
impossible limits, that again indicates that some one of the assump-
tions is inadmissible. As Tromholt does not give in detail, in
Petermann's " Mittheilungen," the 367 measurements at Kouto-
keino, made in order to obtain even 60 corresponding measure-
ments at Bossekop, we can not, at present, know how many nega-
tive parallaxes resulted from his computation ; but the fact that of
these only 42 were deemed reliable enough to be combined into a
mean value, leads us to infer that in this, as in every other similar
work, there was a large proportion of negative parallaxes ; that is
to say, of impossible results.
In an article in the Z. O. G. M., 1882, XVII, p. 343, Tromholt
states that he found the aurora often invisible in Bergen, while it
was visible near by, and concludes that the altitude is, and must
be, small.
Lemstrom.— According to Lemstrom ("L' Aurora Boreali,"
Paris, 1886, p. 50) in the Danish observations at Godthaab, 1882-83,
a base of 58 kilometers was utilized, and they were made simul-
taneously by the use of signal lights, and in the vertical plane
containing the two stations, as well as in the magnetic meridian.
The lowest edges of the auroral bands were always observed.
Thirty-two results were classified as follows :
Altitude
Kilm.
10 gave parallaxes less than 1 degree,
5 " " between 1 and 2 degrees, 67.8 - 45.0
4 " " " 3 and 4 " 38.1 - 9.7
3 " " " 5 and 6 " 9.4 - 74
4 " " M 7 and 8 " 6.2 - 3.7
{10 degrees. 3.22
14 " 2.87
15 " 1-99
1 " parallax " 17 " 1.96
1 " " " 86 " 1.35
1 " " " 143 " 0.61
The altitudes 1.99, 2.87, 3.22 were measurements of the same
arc taken at intervals of two minutes, and the comparison of these
among themselves would seem to show that the auroral light rose
or fell appreciably in two minutes, % at the rate of something like
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THE ALTITUDE OF THE AURORA. ,63
200 or 400 meters per minute, if we may rely upon the determina-
tions of altitude.
BiGKLOW. — Professor Bigelow, in the American Journal of
Science, February, 1891, showed how to utilize the auroral stream-
ers, as distinguished from the arches, in computations of altitude.
He assumes that the streamers agree with the stream lines of the
magnetic field surrounding the earth, and with this simple assump-
tion deduces from the Gaussian theory formulae that apply, prop-
erly speaking, to the normal distribution of magnetism, and like
all other magnetic methods, will be in error in proportion as the
earth's magnetic field is disturbed during the aurora.
Reed. — Mr. M. Reed, of Harvard College Observatory, Cam-
bridge, Mass., in the Bulletin of the New England Weather Service
for April, 1892, calculates the altitude of the east-west arch of the
aurora of April 25th, which passed near the zenith of Mayfield,
Maine, while it was twenty degrees south of the zenith at Cambridge
Observatory. The observations at Cambridge, Blue Hill, and Prov-
idence gave an altitude of 300 miles. The aurora of the next
night, April 26th, was observed at Cambridge and Blue Hill, and
the resulting altitude was 1,241 miles. Blue Hill Observatory is
about twelve miles due south of Harvard College Observatory.
Kramer, Bollbr. — I am indebted to Dr. Bauer for a reference
to an elaborate work by W. Boiler on the "Aurora Australis," pub-
lished in Gerland's Beitrage zur Geophysik, Band III, heft I, pp.
56-130. 1896.
Dr. Kramer of the German naval medical staff (see pages 75
and 128 of Boiler's article) assumes that the magnetic South Pole
is at latitude 75 ° and longitude 125 E., or in the meridian of the
observer who was at longitude 125 14' E. and latitude 35 45' S.
on August 18-19, 1893. He assumes, furthermore, that the auroral
light as seen in the south streamed from the magnetic South Pole
vertically upwards from the earth's surface; that, therefore, the
observer saw it directly south of himself. These assumptions
enabled him to calculate that the observer's horizon intersected
this vertical beam of light at an altitude of 1,945 kilometers above
the magnetic pole (no allowance was made for horizontal refraction),
which would, he says, therefore be the lowest altitude at which the
light could be seen (no allowance is made for the extinction of
light by atmospheric absorption).
Boiler adds to this his own calculation, under the same assump-
tions of the altitude of the upper portion of the light which was
5
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1 64 CLEVELAXD ABBE. [Vol. iil No. 4-]
observed by Dr. Kramer at an apparent angular elevation of 20 ,
and finds 5,654 kilometers as the upper limit. The assumptions
underlying these calculations render the results of no value.
GENERAL SUMMARY.
The several methods that have been suggested for determining
the altitudes of specific features in an auroral display depend
respectively upon assumptions based on preconceived views as to
the true nature of the auroral light and the structure of the arches,
rays, and coronas. These methods may be briefly recapitulated :
1. The Parallax Method. — This assumes that a spot or beam
of auroral light has a definite locus and is a distinct concrete object
that can be simultaneously seen by two or more observers. It is
the earliest method, used first by Halley, Mairan, Maupertuis,
Maier, and Krafft. A hundred years later this method was faith,
folly tried by Bravais and Lottin, at Bossekop, in 1838. The
unprejudiced examination of their observations showed that two
expert observers, ten miles apart, could rarely recognize the same
features for mutual observation with their theodolites. Espy
showed that many previous computations by this method had been
vitiated by assuming impossible identities as to the arches observed
at different stations many miles apart. The Swedish observations
in 1882-3, at Cape Thordsen, Spitzbergen, using a base line of only
•573 meters, led to the same conclusion.
2. Galle's Method.— This assumed that an observed auroral
streamer is parallel to a free magnetic needle on the earth's surface,
vertically below the beam. The observed position of the center of
an auroral corona gives us the dip of the needle suspended in the
region whence that light emanates, while the isogonic charts show
us what point on the earth's surface would have the same dip.
The distance of the observer from that point is the base of a right-
angle triangle, whose vertical side is the desired height of the
aurora. But all observations, as well as Gauss's theory show that
neither the azimuth nor the dip of the needle in the region of the
corona, can agree with that at the earth's surface beneath it, and
that the absolute and differential values are subject to such great
disturbances during auroras that the computed altitudes can have
no reliability.
3. Galle's Second Method.— The general principles of the
first method can be applied to individual auroral beams; but the
computations are vitiated by the same unknown uncertainties as to
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THE ALTITUDE OF THE AURORA. 165
the position of the needle during the magnetic disturbances that
characterize the aurora.
4. Bravais's Method of Amplitudes. — This assumes that
the auroral arch has throughout its whole extent a uniform altitude
above the earth's surface, and, furthermore, that it is simply the
arc of a horizontal circle, so far as concerns the small portion seen
at any one station. By observing the apparent angular altitude
and amplitude of the two ends of the arc and its summit, the linear
altitude can be computed.
Slight modifications of this method have been made as follows :
A. Fearnley assumes that the arch is not a circle, but that it
has the same curvature as that of the magnetic parallel
on the earth's surface through the observer's station.
B. Professor H. A. Newton assumes that the arch has the
same curvature as the nearest part of the normal zone of
greatest observed auroral frequency.
C. Nordenskold assumes that the arch is a circle whose
center is at the northern pole of the zone of auroral fre-
quency; namely, latitude 81 ° N., longitude 8o° W. This
same assumption is adopted by Carlheim-Gyllenskold.
D. T. Bergman assumes that the arch has its summit in the
astronomical meridian, and that it is circular with its
center at the geographical North Pole.
5. Bravais's Method by the Apparent Breadth of the
Arch. — This assumes that an arch is everywhere of uniform actual
width, and parallel to the earth's surface. Computations by this
method were made both by Bravais in 1838, and Gyllenskold
in 1883.
6. Bravais's Velocity Method. — The apparent velocity of
the movement of the arch in the magnetic meridian, northward or
southward, when observed at two stations, distant from each other
in the magnetic meridian, so that at one station the arch appears
much nearer to the zenith than at the other station, gives a method
of computing the height.
7. In my memoir on the aurora of 1874, I pointed out the fact
that the motion of waves along an arch, eastward or westward, as
observed near the zenith, may be assumed to coincide with the
motion of the columns or rays along the same arch when seen at
a distance from the zenith, especially to the northward. Two
observers, therefore, determining the apparent angular rate of mo-
tion along the arch, as nearly simultaneously as possible, have the
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166 CLEVELAND ABBE. [vol. hi, no. 4 .J
data for determining the altitude under the assumption that they
are examining the same object. Gyllenskold computed the alti-
tudes for 156 arches, based on the north-south motions. I do not
know of any computations based on the east-west motions.
8. Gyllbnskold's Method by the Apparent Length of
the Auroral Beam at Different Apparent Altitudes. —
If we assume that the beam is a concrete object moving parallel to
itself and to the free needle, then, as it approaches the zenith of the
observer, its apparent length, or rather the apparent altitude of its
upper and lower end, will change. Assuming that its own linear
length remains the same, then two observations at the same sta-
tion of the apparent altitude of the top and bottom, at two suc-
cessive intervals, gives us the means of determining the actual
length and altitude. On the average of the beams observed by
him, Gyllenskold finds for the lower end an altitude of 264 kilome-
ters, and for the upper end, 372. Iyoomis applied the simple parallax
method to the observations of the upper and lower ends of auroral
beams, assuming that observers several hundred miles apart were
observing the same delicate extremities ; he deduced, for one case,
the elevation of the lower end of the beam 49 miles, and for the
upper end, 841 miles.
********
All these and the various other possible modifications of meth-
ods, besides assuming more or less doubtful properties, agree in
one fundamendal assumption ; namely, that the definite beams and
arches that we attempt to observe so accurately have an individual
existence and a definite locus. If this fundamental assumption falls
to the ground, then all our ideas as to the location and the nature
of the auroral light must be given up, and we must start the
investigation de novo.
That this assumption must be given up seems to be a necessity ;
it has, indeed, already been relinquished by some, but the demon-
stration has not been made so logical and convincing as is now
possible. The fact that different observers a few miles apart do
not see the same features has been recognized; but it was supposed
to be explained by the general fact that the auroral light was so
low down that the observers could not see the same features, and
that it is only when the aurora is very high that the same feature
could be observed simultaneously, just as two observers five miles
apart rarely see the same cumulus cloud simultaneously. It has
even been suggested that the auroral light, moving rapidly along,
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THE ALTITUDE OF THE AURORA. 167
might present the same aspect to observers a few miles apart
within a few minutes, thus explaining the diversity of computed
altitudes.
But all these ideas acquire a precise significance when we
examine critically the most careful observations that have been
recorded, and most of which I have summarized in the preceding
pages. There is no doubt but that the light out of which the
auroral phenomena are formed emanates from a certain circum-
scribed region, but the point of special inquiry is as to whether the
well-defined streamers, beams, waves, and arches of light on which
our observations are made have a definite locus. These appear so
sharp as to be subject to exact observation. Do such observations
demonstrate that they have an exact locus ; and, if not, what do
they teach us?
Bravais and Lottin, occupying stations at Jupvig and Bossekop
respectively, 15,625 meters, or about nine and one-half miles apart,
making observations on the angular altitude of arches, so definite
that an error of 0.2 of a degree is not to be expected, derived the
following parallaxes :
1839— January 12, -3 42' January 21, -i° 34'
+2 13 +1 04
+9 52 +0 45
-o 08
Similar figures have been quoted in our previous pages, as
deduced by Gyllenskold from his parallax work in 1882-3, when
the two observers were much closer together than Bravais and
Lottin, namely, 573 meters, or one-third of a mile apart. These
forty-two measurements may be arranged in the order of magni-
tude, as follows :
-8°.55
-6-35
-1 .00
-1 .00
-0.58
-o .50
-0.47
-o .40
-o .30
-o .27
-o .25 -o .05
These latter more numerous observations, like those of 1839,
show a large number of negative parallaxes; in fact, there are
twenty-€ve negative as opposed to seventeen positive parallaxes.
Now every negative parallax means a physical impossibility. So
far as we know, negative values could only result from an error in
-0°.22
-o°.<>5
-ho°. 3 o
-O .20
-O .05
+0.35
-O .19
-O .04
+0.40
-O .17
-|-o .01
+1 .05
-O .17
+0 .03
-t-1 .05
-O .16
-|-o .10
+1 .55
-O .12
+0.16
4-2 .00
-O .IO
4-o .20
+ 2 .29
-O .09
+0 .20
+4 41
-O .06
+0.23
+5.50
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1 68 CLE VELAND ABBE. [Vol. hi, no. 4 ]
in the identification of the arches or an error in the measurement
of the angles, or a want of simultaneity in the observations at the
two stations coupled with a change in the position of the arches,
or, finally, an error in the fundamental assumption that the ob-
servers are looking at the same object.
If all the arches were at a very great or infinite distance, the
parallaxes would be either zero or small plus or minus figures, de-
pending on the accuracy of the work ; but when we turn to the
original records of the observations, as quoted before, we find that
the large positive and negative values are often closely associated to-
gether. If we had not the assurance that all these observations were
made at times when the arches were clearly identified and were not
in rapid motion, and were sharp enough to be capable of exact meas-
urement — if we had not the assurance that there was no chance of
an error of from one to nine degrees — then we might dismiss the
subject with the feeling that the altitude of the aurora is indefinite
and variable and can not be accurately examined. In the absence of
these exact observations, several such conclusions have been adopted.
Thus, one concludes that the auroral light must have been subject
to rapid movements up and down, towards and from the observer;
another, that the auroral light is sometimes low down and sometimes
high up ; Gyllenskold, believing the aurora to be very high up, re-
jects the largest parallaxes as probably erroneous, and holds to the
small ones; Andr&e rejects the small ones as too small to be accu-
rately determined, and adopts the larger ones as perfectly credible.
Every attempt to reconcile the discrepant parallaxes plunges us
further into hypotheses as to the accuracy of the work, that are
not warranted by the steady appearance of the aurora and the well-
established accuracy of the observers.
The straits to which one is reduced in order to reconcile these
accurate observations with the hypothesis that the arch is a con-
crete object having a definite locus, is well illustrated by Gyllen-
skold's final computation and conclusions. (See the Swedish Re-
port, Vol. II, Part i, p. 178.)
" I have divided the total number of parallaxes into two groups,
according as the angular altitude of the arch was greater or less
than forty-five degrees. Thirty-two observations upon arches whose
apparent altitudes lay between o° and 37 °, give me a mean angu-
lar altitude of 14 19' and a mean parallax of minus — 2.7', plus or
minus 4.2'. Six observations on arches between 64 and 79 give
me a mean angular altitude of 76 10', and a mean parallax of
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THE ALTITUDE OF THE AURORA. 169
+ i° 43', plus or minus 6.7'. By accepting, within the limits of the
probable errors, those values that accord best with each other —
namely, + 1'.5 and + 1 ° 36' — we find for the arches situated near
the horizon an elevation of 81.9 kilometers, and for those near the
zenith an elevation of 19.8 kilometers at the maximum. These
parallaxes, if we take account of the different weights of the ob-
servations and suppose the mean values to have a weight propor-
tional to the number of observations, give for the aurora borealis
a mean altitude of 72.2 kilometers.*'
In the above computation the fundamental principles of the
method of least squares seem to be entirely disregarded. As I
understand this subject, the probable error, ±4.2', shows that the
parallax — 2.7' has no appreciable value as compared with 0.0'.
The negative sign — 2.7' shows that the observations demonstrate
that there was no appreciable parallax as compared with some
source of error that has forced a negative, that is to say, an im-
possible result. The frequent occurrence and the large value of
these negative parallaxes leave no doubt that this unknown source
of error has always been present, and often amounted to a large
quantity. But, on the other hand, the error could not have arisen
from the identification of the arches or any other feature in the
work of the observer, and there is but one conclusion possible;
namely, that the fundamental assumption is unjustifiable and con-
trary to nature.
As regards the assumption that the auroral arches are definite
concrete objects, it is evident that if true, the general appearance
of the arches would not be wholly dissimilar at stations a few
miles apart. Now, in 1838, Bravais expressed the opinion that the
failure to get good parallaxes was due to the fact that Bossekop
and Jupvig, nine miles apart, were too near together, and that
Bossekop with Koutokeino, sixty-six miles apart, would be a better
combination. But, in 1883, Tromholt at Koutokeino found as
much trouble in identifying the arches observed by himself and
by the Norwegians at Bossekop as had been found by Bravais in
1838, and distinctly says that all attempts to utilize the simulta-
neous observations made at Sodankyla, about 150 miles southeast
of Koutokeino, were useless, apparently on account of the diffi-
culty of identification at simultaneous times. I may remark that
the average parallaxes deduced for the sixty-six-mile base line used
by Tromholt, for the twelve-mile base used by Bravais, and for
the third of a mile base used by Carlheim-Gyllenskold, iespect-
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170
CLE V ELAND ABBE. [vol. in, No. 4.)
ively, overlap each other so much as to show that the so-called
parallax does not necessarily increase with the increase in the length
of the base line; in other words, it can not possibly be a true
parallax.
The only doubt left is as to whether the aurora is so low down
that neighboring observers do not see the same features, or whether
it is some form of optical illusion, such that each observer sees his
own personal series of phenomena; or whether, perhaps, both of
these are true, and combine to deceive us in every case. The
former of these alternatives appears to be negatived by the de-
scriptions given by observers a few hundred feet apart ; they see
similar phenomena, and yet their accurate measurements give
great negative parallaxes. Of course, some measurements give
positive parallaxes, and these do not contribute to settle our di-
lemma, but the great number of negative parallaxes are real
quantities of the greatest value in deciding our question. The
measurements can not be gainsaid ; the negative results, oftentimes
quite large, have a real value and must be explained. If the ob-
servers are too near together to justify the assumption that they
are looking at different arches, then the only conclusion possible
is, that they are both looking at the same thing, and that it really
has a negative parallax; that is to say, it is not above them, and
does not exist in reality where it appears to be, but is some form
of optical illusion.
There are doubtless many forms of optical illusion present in
the aurora, such as the perspective phenomena to which are due
the corona, the curvature of the arches, and the spreading of the
beams; there may be other forms, especially, perhaps, those due
to alignment or position and to undulatory interferences. Without
presuming to have established the real nature, I may suggest the
following hypothesis as worthy of experimental investigation :
A. — If the auroral light is low down, then we must view the
light as due to a discharge of electricity in dusty moist air under baro-
metric pressures that are much higher than those that are needed in
the Geissler tube to produce optical phenomena in clean dry air under
low atmospheric pressure. We can not argue that the low press-
ure is needed in the Geissler tube, and therefore in the aurora,
but must ignore the dry air, and consider the aurora as a discharge
within a region in which the aqueous vapor pressure, or the press-
ure of some other essential vapor or gas, is very low, and the vapor
itself is in the form of crystals, such as the spiculae and needles of
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THE ALTITUDE OF THE AURORA.
171
ice. We must consider the auroral light and the electrical luminos-
ity of clouds as simply another form of lightning. Apparently,
the formation of lightning attends the formation of drops of water
at temperatures above freezing, but it is known to be milder in
proportion as the dew point is lower and the drops are smaller;
when the temperatures are below freezing and the raindrops
turn into spiculse of ice and crystals of snow, we have the au-
roral phenomena. Any electrical discharge into or through the
atmosphere — no matter how it originates— may form auroral light
when the vapor tension, not the dry air tension, is low enough.
The details as to the molecular phenomena will eventually be
worked out; but at present it suffices to quote the remarkable
broad band of lightning, photographed by Jennings of Philadel-
phia, which gives us a close imitation of the appearance of the cur-
tain aurora at any instant. The cool moist climates are those
which, of all others, have ever been distinguished for brilliant au-
roral displays. In such regions, at a slight distance above the earth's
surface, masses of moister air are mingling with those of drier
air, and, as Espy first pointed out, moisture is diffusing into the
drier regions, and particles of fog and haze are freezing into hazy
clouds of ice spiculse and snow. As the magnet gathers iron
filings into familiar curved lines of force, and as the earth causes
by its magnetism our little magnetic needles to range themselves
into the same curves, so it also acts upon the electrified ice parti-
cles of the atmosphere, and arranges them in the lines and in the
order that allow of the easiest discharge of their own electricity.
Numerous studies of auroras have convinced me that the auroral
light emanates from this aqueous material lying at the confines of,
or between, currents of air having very different temperatures and
relative humidities, and flowing over each other, or mingling at
their boundaries as a part of the general circulation of the atmos-
phere between temperate and polar regions and between areas of
high and low pressures. The precise characteristics of the elec-
trical process remain to be investigated ; but the outcome of it all
is, that a layer of air is formed, full of electrified spiculae, which
are arranged in order by the influence of terrestrial magnetism, and
especially as modified by the electro-magnetic disturbances that per-
meate space, and, in part at least, seem to emanate from the sun.
The observer's line of vision, penetrating this region, sees here
and there combinations of special bright beams, such as are formed
by the alignment of several luminous lines standing behind each
6
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172
CLEVELAND ABBE.
I Vol ni. No. 4- J
other. If the minor lines are arranged in folds, and more or less
irregular cylindrical surfaces, then, wherever the observer's line of
sight runs tangent to the cylinders or the sides of the plications,
the luminous surface at once becomes condensed by alignment into
a beam or streamer or arch that is well defined on one side and diffuse
on the other. There may be a few or there may be many folds in
this layer, and observers, only a short distance apart, looking up
into this broad layer of haze, will see different aspects of the folds
above them; they may see the same streamer or arch, with slightly
modified appearance, or may see entirely different streamers and
arches, according to the style of the plication. Thus, in the accom-
panying diagram (Figure 3), if there are many short folds in
A ' \ ,"' ^
Figure 3.
the layer of light, as at A, B, the observer at O will see at
/, 2, j, three beams, if the folds are in a vertical plane, or three
arches if they are in a horizontal plane; and another observer at
P will see two beams or arches at 4 and 5.
If there is only one large, decided horizontal fold, as at C D
(Figure 4), the observer at R will see but one arch as at 6, and
observers either side of him for a little distance will see the same
Figure 4.
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THE ALTITUDE OF THE AURORA.
1 73
arch, but feebler and broader; observers farther away will see no
arch until we reach a great distance, as at S, where two small
arches may be seen at 7 and 8 ; or, still further, at T y where one faint
arch may be seen at 9 and possibly one at 10.
A broad expanse of atmosphere, perhaps one-half of the temper-
ate zone, may be covered with such a layer of luminous lines within
which auroral beams and arches are observable. As the individual
lines and beams of light are approximately parallel to the free
magnetic needle in their localities, that fact — together with the
effects of perspective — will determine their apparent angular posi-
tions, as seen by any observer. On the other hand, the arches, as
seen by us in the distant north, generally represent the total
effect of a great number of lines, as seen from a long distance to
the south. The definite lower edge of an arch represents the lower
ends of the lines, or the lower surface of the layer of mixtures
within which the light originates. If this lower surface is undula-
ting, as at E F (Figure 5), then, the observer at T sees an arch
T &
Figure 5.
having its lower edge at //; and again another having its lower
edge at 12, both to the north of him, and better defined below
than above. But an observer at U sees an arch to the south of
him, at ij t and another to the north, at 14.
As these undulations in the lower surface may be as numerous
as the parallel bands of cirrus haze, and as they must depend partly
on the relations of the atmosphere to the ground, there seems to be
no limit to the varieties of illusions produced by alignment and
perspective that may be introduced into the auroral phenomena.
It may even happen that several layers of mixtures are in progress
simultaneously, one above the other, and that each is contributing
its own auroral phonomena.
The conditions under which negative parallaxes may occur can
now be easily seen ; it is entirely a question of the position of the
observing stations relative to the folds that form the arches and
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1 74 CLE V ELAND ABBE. [Vol. hi, No. 4)
beams ; thus in the layer G H (Figure 6) we have two folds at nearly
the same distance apart as the observing stations V and IV, so that
Figure 6.
the sight lines, V ij and W 16 , when combined together, give a
zero parallax. Any other stations V and W\ a little to the right of
V or to the left of W, would give a negative result, because the
stations would be nearer together than the arches above them. If
a series of measures be made at V and W, in rather rapid succes-
sion, and if, as is usually the case, the arches — viz., the folds — are
moving southward or northward with an irregular motion, then
some of the simultaneous observations will give positive and some
negative results, owing to the varying distance between the two
folds.
A simple way to test these views, and the reality as well as the
identity of the auroral arches is to provide, at least three stations
at a short distance apart in the magnetic meridian, at each of which
simultaneous drawings and measurements are to be made. The
middle station will always serve as a check to show whether the
end stations are observing the same arch. Thus in the last sketch,
(Figure 6), the observers at J 7 and Ware supposed to combine the
observations of their arches 15 and 16, whereas if they had com-
bined their arches V ij and W 18, or V 17 and W 16 1 they would
have found positive parallaxes, and fair approximations to the alti-
tudes of the layer of light. Even better would it be if the ob-
server at W should begin his work when standing beside the
other observer at V, and then move slowly towards W, watching
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THE ALTITUDE OF THE AURORA. r75
the arc V ij, until he sees it disappear a long time before he reaches
IV. It is only in case the arc at V 15 has continued clearly visible
without interruption until he reaches W that he is justified in meas-
uring it from that point for parallactic computations.
When observers are close together, and especially when in tele-
phonic connection, it has been customary to attempt to secure per-
fect simultaneity in the observations for parallax, and this is cer-
tainly important in view of the possible movement of the arch.
On the other hand, when observers are far distant, and the phe-
nomena as described differ at each station considerably, it has
been considered that simultaneity is an important factor in helping
to identify, or rather to demonstrate the identity of two observed
arches. The argument seems to be that different things can not
exist in the same place at the same time; the arches are seen at the
same time, and, therefore, they must be in the same place. Of
course, this argument falls to the ground when, by comparing the
simultaneous records from a large number of stations, we find utterly
diverse appearances observed at each. Stations far apart appear to
see the same arch, while several intermediate stations near together
see nothing of that, but a variety of other phenomena. Simultaneity
is, therefore, not a criterion as to identity. The results deduced by
Tromholt from Bossekop on the north and Sodankyla on the south,
with Koutokeino between, fully confirm Espy's study of European
auroral arches, and my own study of the American aurora of
April, 1874.
The auroral sky is but a series of luminous waves or zones in
the midst of a general diffuse light. It matters not whether the
brighter zones are due to perspective alignment or wavy surfaces
or optical or electrical interferences ; in either case observers are
liable to great confusion in attempting to identify them.
A general test as to the existence of illusions due to alignment
or perspective, can best be effected in the following way : Let four
observers confer together at one station; select a single narrow
beam or arch for study, draw it upon a map of the stars, and com*
pare the four drawings to be sure that there is a perfect understand-
ing ; then separate in four rectangular directions for half a mile or
less, make another set of drawings simultaneously, and return to
the starting point, where a third set is made simultaneously, noting
also the especial changes that take place in the auroral light dur-
ing the trip out and back. The separation and return can be done
quickly by the use of the bicycle or tramway. The comparison of
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1 76 CLE V ELAND ABBE. [Vol. in, No. 4.]
the four sketches will enable one to distinguish between the effects
of alignment and of parallax.
As there is a possibility that some additional form of illusion is
present in the interior structure of every electric discharge through
gases, this matter could be tested by determining the parallax by
observations upon one of the bands of light seen in the Geissler
tube. A short base line at a known distance from the tube should be
used. If the computation locates the light entirely outside of the
tube, we shall, of course, be forced to the conclusion that from
these two points of observation we see entirely different bands of
light within the tube. Even without apparatus an observer by
closing each eye alternately may possibly perceive a change in the
appearance of the bands in the Geissler tube.
ADDENDUM.
Having just received the third volume of results of the Inter-
national Polar Expedition sent out by Finland in 1882-84, under
the general directorship of Professor Selim Lemstrom, I take pleas-
ure in adding the following extract translated from pages 15, 16,
of the last section of this volume :
" During the first year we had made an arrangement with the
late M. Tromholt at Koutokeino to observe simultaneously the
angular altitude of the aurora borealis in the vertical circle passing
through that place at a certain definite time, and this is the reason
why our own independent determinations of the altitude of the
aurora were only made on one occasion, but as this gave quite an
extraordinary result, we give it in detail.
" Two theodolites provided with telescopes, and vertical circles
were established respectively at our central station, Sodankyla, and
at Kelujoki, a distance of about 4.5 kilometers toward the north,
where the Kelujoki empties into the Kitinen. By utilizing the
conducting wire employed in measuring the north-south earth cur-
rent, the two stations could communicate by telephone, so that the
observations were made in accordance with telephonic signals.
M. Biese observed at the southern station, and Petrelius at the
northern station. The aurora borealis appeared in the north with
a soft light changing a little from time to time."
"About 6.40 P. M., Gottingen mean time [date not given],
everything was ready for measurements, and little by little the
aurora had increased in brilliancy and risen high up in the sky,
still showing in general the form of an arch, but preserving its
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THE ALTITUDE OF THE AURORA,
177
vacillations. As soon as one saw a single arch, immediately it
would divide into two, the upper one of which, especially, would
show a tendency to transform itself into an undulating band, and
once, at least, in reality took on this form. To the northeastward
one could see some auroral rays entirely separate from the rest oi
the phenomenon. The measurements were made by telephonic
signals in such a way that the pointing and setting was done
simultaneously at the two stations. The determination of the point
to be observed, which preceded each pointing, was so precise that
the observers themselves considered it as impossible that there
could be any error as to the part of the arch they were measuring.
The measurements occupied about half an hour, and the settings
were always made upon points located on the lower side of the arch.
"The observations numbered 1-5 and 8 relate to the ordinary
arches ; observation No. 6 was made upon the undulating band,
and No. 7 upon a band in the form of an arch. The measure-
ments were as follows :
NO.
ALTITUDE ABOVE THE NORTHERN HORIZON OP THE LOWER
EDGE OF THE ARCH
Southern Station
Northern Station
Difference
I
7° 16'
7° if
+ o° i'
2
9 37
8 48
— 49
3
II 19
8 24
— 2 55
4
12 17
9 5i
— 2 26
5
12 49
10 45
— 2 4
5 19
6 58
+ 1 39
ALTITUDE ABOVE THE NORTHERN HORIZOl
* OF THE LOWER
EDGE OP THE BAND
6
io° 13'
6 38
7°37 /
- 2° &
7
2 31
— 4 7
As an average result we obtain the following parallaxes:
For the arch . . . — 1° 38' from five observations.
-+-1 37 from one observation subsequently.
For the undulating band — 3 21.5, from two observations.
" It is quite remarkable that the phenomenon does not seem to
have had the same appearance as seen from the two stations, not-
withstanding that their distance apart was so small. This fact was
ascertained with certainty at their sixth observation.
"The observer at the northern station, Kelujoki, really saw
an undulating band separating from the other phenomena, but did
not find it marked by an intensity greater than that observed ear-
lier nor by bright colors.
"At the southern station, on the contrary, we observed on this
same occasion an intensity greater than at any other moment during
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1 78 CLE V ELAND ABBE. [Vol. in. No. 4 J
the evening. The band appeared of a bright greenish yellow, with
the lower border distinctly red. Although the observer, Petrelius,
at the northern station, had already had occasion to observe this form
of aurora, and he was well able to distinguish the colors, yet the
command to set upon that portion of the band where it appears red,
caused him much surprise ; for he could see nothing of the red.
"Assuming that the two observers had actually seen the same phe-
nomenon, the above parallaxes, except No. 8, would all be absurd •
for if the arch of the aurora was even at an infinite distance, the
angles observed at the two stations would have been the same ; if
it were nearer than this, the angular elevation at the northern sta-
tion would have been greater than that at the southern ; but in
place of this the angle at the northern is smaller than at the south-
ern ; it follows, therefore, that the two observers did not see the
same phenomenon. Another proof of this fact is that at the south-
ern station the aurora was seen distinctly red; but not so at the
northern station.
"Whenever two observers at a distance of 4.5 kilometers see dif-
ferent phenomena, it is quite clear that determinations of parallax
made with much larger bases must be uncertain if .not altogether
illusory."
(The above extract confirms the conclusion previously stated
that the only remaining method of settling the question as to the
existence and reality of the parallaxes must consist in an arrange-
ment by which several observers, standing together side by side,
agree upon a definite point for measurement. After each has made
his measurements, they must then separate in different directions
for short distances, make the necessary measurements simultane-
ously, and return to the same spot, where the measurements
should be again repeated simultaneously. We shall thus obtain
the data for determining the accuracy of the measurements per se,
the changes in the apparent position of the auroral spot, and the
resulting parallax, if any.
The differences in the colors observed at two stations so near
together serve to throw great doubt upon the possibility of any
measurable parallax in the strict sense of the term, but confirm
the suggestion, made by me many years ago, that we may have to
do with a phenomenon analogous to optical interferences, although,
of course, so different from it that the use of that term seems quite
inappropriate.)
August 25, 1898.
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BIGELOW'S " SOLAR AND TERRESTRIAL MAGNETISM."
Reviewed by Arthur Schuster, F. R. S.
Professor Bigelow has on various occasions published the con-
clusions drawn by him from his magnetic investigations, but so
far the details given were not sufficient to allow an independent
reader to form an opinion as to the value of his work. I am glad,
therefore, to find that the United States Weather Bureau 1 has
now enabled Professor Bigelow to supply the omission ; and in the
small volume which has recently been circulated, those interested
in the subject will find ample material whereon to base their judg-
ment.
I may say at once that although I have to criticise severely
some of Professor Bigelow's conclusions, and am obliged to put
myself into antagonism to every one of his results, I am fully
sensible of the great service rendered by the author in collecting
together and reducing a most valuable series of facts and observ-
ations.
As Professor Bigelow's main contention lies in the assertion of
a direct magnetic action of the Sun, it will be useful to consider,
in the first instance, what effects such a direct action can produce.
Considering the distance and size of the Earth, any magnetic
force due to the Sun must be sensibly the same in direction and
magnitude all over the surface of the globe. If the Sun be mag-
netized parallel to his axis, we may, following Lord Kelvin, 2 de-
compose the action into components parallel and perpendicular to
the earth's axis. Owing to the changing distance between the
Earth and Sun, the former would yield a small periodic annual va-
riation, directed towards the geographical north, while the second
component would produce a daily variation, having the sidereal day
for its period.
If the Sun is magnetized transversely, additional periods are
introduced by his rotation. It has been commonly assumed that
the duration of the period caused by the rotation of the Sun is the
synodic time of revolution ; but calculation shows that this view is
incorrect, and that, on the contrary, no appreciable periodicity of
i "Abstract of a Report on Solar and Terrestrial Magnetism in their Relations to
Meteorology." United States Weather Bureau Bulletin, No. 21, Washington, 1898.
*Proc. Roy. Soc. Vol. UI, p. 305 (1889); Nature, Vol. XLVII, p. 108.
7 179
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180 A. SCHUSTER. [Vol. hi, no. 4 .j
26.8 days can possibly be caused by any conceivable magnetization of
the Sun. The strongest period due to solar rotation has a time of
about 28.5 days, and there is a second period of smaller amplitude,
the time of which is that of sidereal revolution. An important
characteristic of these periods is that the forces act in the magnetic
meridian, and that the horizontal components must vary as the
cosine of the latitude, while the vertical components vary as the
sines. There can be no components towards the geographical
west.
I may now proceed to discuss how far the effects which Pro-
fessor Bigelow ascribes to the magnetization of the Sun agree with
those which calculation declares to be possible.
In the second chapter examples are given of the tabulations
which serve as basis to Professor Bigelow's work. After making a
certain allowance for disturbances, the average daily value for the
magnetic elements was calculated. The monthly mean of these
daily values was taken to represent the " normal " value for the fif-
teenth day of the month, and interpolating between the fifteenth
days of successive months the " normal " values for each day were
calculated. The difference between the vectors representing the
normal and actual observed forces represents what Bigelow calls
the deflecting vector, the periodicities of which are to be examined.
If the angles which the deflecting forces form with the geo-
graphical meridian are arranged in tables, it is found that there is a
certain persistency in them, the forces acting towards the north for a
number of successive days, and such periods being succeeded by
others in which the deflecting forces act southward. From this
the author concludes that there must be a definite periodic disturb-
ance acting on the needle, and by a method which must fail when-
ever there are several overlapping periods determines the time to be
26.67928 days. This figure agrees remarkably with the synodic
revolution of the solar equator, and hence the conclusion that there
is direct magnetic action of the Sun observable on the Earth. I
have mentioned above that mathematical analysis declares it to be
impossible that a period equal to that of the synodic revolution
can be produced by such a direct action, and Professor Bigelow
must be wrong, therefore, either in his periodicity or in the conclu-
sion he draws from it. But the author's periodicity is not a period-
icity of the ordinary kind, for it shows an " inversion ;" that is to
say, at certain intervals the maxima changes into minima, and
vice versa. There is here a confusion of terms.
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BIGELOW' S MAGNETIC WORK. 181
If a quantity is said to be periodic, it can only mean that at in-
tervals equal to the length of the period the quantity repeats itself,
and goes on repeating itself forever ; there is no room for such an
inversion as Professor Bigelow speaks of, and the very fact of the
inversion disproves the periodicity. As the matter is of great im-
portance I must enter into it a little more fully, although Lord
Rayleigh has already repeatedly drawn attention to the importance
of keeping our ideas clear on the subject. If a variable shows a
periodicity of time %*/&, it can only mean that the analytical rep-
resentation of the variable contains a term cos (kt+a) f and it can
mean nothing else. Such phenomenon as that called inversion by
Professor Bigelow can only be produced by the superposition of at
least two different periods :
cos kt -f cos qt = cos (p — q)t cos (p+q) t
2 2
If p and q are nearly equal, the first factor varies very slowly, and
after a certain length of time changes sign. During a limited in-
terval we may then speak approximately of a periodicity 4^/P+q,
and if we compare times at which the first factor is approximately
-f i and — i, we get apparently such a change of phase as the author
calls an " inversion."
Two tuning forks having frequencies 256 and 252 would, ac-
cording to him, be periodic with a frequency 254, the periodicity
showing an " inversion." But such a manner of speaking would
bring total confusion into a subject, in which clear ideas are essen-
tial. The one fact which seems established by Professor Bigelow's
tabulation is the absence of a 26.68 day period, and his position is
really saved hereby, as he will still be able to believe in a direct
magnetic action of the Sun ; for the two periodicities T u T t which
a magnetized Sun could produce are related to the synodic period
T by the equation :
2 \T t + TJ ~ T
2 \T t ' TJ T
so that if they were of equal amplitude " beats " would result which
might be the cause of some such variation as Professor Bigelow
believes he has discovered. One of the two periodicities has, how-
ever, an amplitude equal to three times that of the other, and with-
out a very careful analysis it is not possible to declare whether they
really exist or not.
* In Chapter III we have some vague reasoning from which the
conclusion is drawn that the disturbing forces are due to solar
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1 82 A. SCHUSTER. [vol. in, No. 4 )
action. But as these forces do not at all conform to the criterion
pointed out above, that the north force should vary as the cosine
of the latitude, and the vertical force as the sine, and as no attempt
is made to separate by a vigorous analysis the outside from the
inside force, we need not attach any value to the author's astound-
ing conclusion that " the nucleus of the earth is impenetrable to the
lines of magnetic force.' '
The most surprising of Professor Bigelow's conclusions are
reserved for his Chapter IV, in which an attempt is made to account
for the diurnal variations by means of a direct solar action. It is
of course obvious that no ordinary magnetic influence emanating
from the Sun can explain the diurnal variation, and Professor
Bigelow has to invent therefore a force unknown so far to physics.
The author's views are so peculiar that they must be quoted in his
own words :
" The diurnal vector system depends exclusively upon the Sun's
electromagnetic or sunlight field, which is a radial field and appar-
ently induces in the ether an efficient polarization in respect to
exploring magnets on the surface of the Earth. ,, (P. 17.)
"The immense rapidity of the vibrations of light in the case
of a train of waves from the source to the observer, practically
integrates the system into a type of polarized ether." (P. 34.)
"The electromagnetic theory of light implies the existence of
a magnetic field practically uniform in force and direction rela-
tively to any magnet large in comparison with the wavelength of
light, and hence to any magnet except of atomic and molecular
dimensions." (P. 81.)
"The vibration is so rapid that the train of individual waves
merges into a steady field in its action upon the Earth as a magnet
or to the exploring magnets employed in observations." (P. 81.)
Whatever meaning the author may attach to these passages,
they sound — to speak plainly — like nonsense to the ordinary reader.
This new force is said to be implied by the electromagnetic theory
of light, but though the author gives three pages of formulae quoted
from Heaviside's papers, there is not one of them that can justify his
assertion. For, surely, Professor Bigelow does not take the quantity
/*, on page 166, to be a magnetic force, as it means a very different
thing, being of different dimensions. Quite apart from any theo-
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BIGELOW S MAGNETIC WORK. 183
retical justification, we may be allowed to ask whether Professor
Bigelow would expect a stronger or different diurnal variation if
the magnets were suspended in sunlight, or whether he would
expect that variation to disappear completely if the magnets were
placed inside a closed metallic box which is known to be opaque to
electrical vibrations? If the author can surmount this difficulty,
will he explain how a force acting along the rays emanating from
the Sun can produce simultaneously a westerly deflection in the
northern and a southerly deflection in the southern hemisphere?
Incidentally we may notice another startling assertion, that the
interplanetary medium is cooled down by the passage of electro-
magnetic waves, and in support of this, one of Heaviside's equations
is quoted, which has no connection with the subject.
Chapter VIII contains a further list of astonishing results.
The magnetic period, which he ascribes to solar action, is not repre-
sented by a simple sine curve, but possesses within the period of
solar rotation 9 maxima and 9 minima. Great importance is at-
tached to these maxima, as they are all " inverted " together, and
different meteorological phenomena are supposed to show a similar
number of oscillations. The curves given on pages 44 and 119
leave no doubt that the author really believes that the Sun in his
rotation can produce such a complicated effect. If A denotes
the solar longitude, the solar action must, according to Professor
Bigelow, contain an appreciable term cos 9X, and probably terms
involving even higher multiples of A. If magnetic forces of this
character exist, the theory of the potential teaches us that they
must diminish very rapidly with the distance, more rapidly at any
rate than the inverse 10th power. The ratio of the average dis-
tance of the Earth and Sun to the solar radius being 229, the force
at the surface of the Sun must be at least (229) 10 times the force
on the Earth. Professor Bigelow's diagram allows us to make an
estimate of the amplitude of the coefficient of cos 9X, which
is certainly greater than .00002 C. G. S. It follows that at the
Sun's equator the magnetic field must be equal to not less than
16X10 8 C. G. S. units, or 8X10 14 times greater than any magnetic
force which has been observed between the pole pieces of the most'
powerful electromagnets.
• If Professor Bigelow's curve is true, the Sun must be sliced like
an orange, alternate slices having positive and negative polarities
of the enormous values just mentioned.
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ABSTRACTS AND REVIEWS
Eixis, WnxiAM, P. R. S. On the Relation between the Dinmal Range of
Magnetic Declination and Horizontal Force and the Period of Sun-
spot Frequency. Proa Roy. Soc, London. VoL 63.
In a paper printed in the Philosophical Transactions of the Royal Society
for 1880, the author compared the diurnal range of the magnetic declination
and horizontal force, as observed at the Royal Observatory, Greenwich, during
the years 184 1 to 1877, with the corresponding numbers of the sun-spot fre-
quency as determined by the late Dr. Rudolf Wolf, of Zurich. The present
communication supplements the former one by incorporating into the dis-
cussion the Greenwich magnetic and the Zurich sun-spot observations that
have accumulated between 1877 and 1896, and tabulating a strictly comparable
series of numerical results for the 56 years from 1 841 to 1896.
Throughout this period the results show an entire synchronism between
the irregularities in the length of the sun-spot period and the magnetic pe-
riod. The accord between the two phenomena, both in period and activity,
is so complete as to indicate either a direct relationship between them or the
existence of some common cause producing both.
Among the uncertain results is a suspicion that the period of these phe-
nomena, which is commonly called the eleven-year period, but which varies
in length to the extent of several years, decreases in length for several pe-
riods, then increases for several periods, and so on.
The conclusion formerly reached that the magnetic effect follows the
sun-spot effect, so that a " lagging " of the magnetic effect exists, is not borne
out by the present extended comparison ; and it seems doubtful, without a
yet more extended series of observations, whether any definite lagging can
be said to exist G. W. Littlehalks.
Nippoxdt, A. Neue allgemeine Erscheinungen in der taglichen Variation
der erdmagnelischen Elemente. Annalen d. Hydrographie u. Maritimen
Meteorologie. 1898. No. III.
The declinations of the needle observed in Pavlovsk, in the year 1882-83,
are discussed as follows : All of the observations for the daily variation in
the declination during one month are united and expressed by a formula in-
volving sines and cosines of the variable x up to the fourth multiple. The co-
efficients of these developments were then plotted as a curve, the abscissae
being the time, and the ordi nates the value of the coefficient for the twelve
different months. Observations made at Tiflis, Wilhelmshafen, Southern
Georgia, Port Rae, and Greenwich were treated in the same way. The follow-
ing conclusions are reached :
1. The law of the annual change of the coefficients in the formula for the diur-
nal variation of the declination grows more complicated, the higher the order of the
coefficient. 2. In all of the stations investigated, the variation of the lower coeffi-
cients can be represented as a combination of a wave of period twelve months with
one of period four months. 3. The law of annual variation for the lower coefficients,
and therefore the influence of these changes upon the daily variation, is the same
for the whole earth. 4. The wave w t containing only the simple multiple of x is
due to geometrical causes such as follow from the position of the earth in space. 5.
The wave w, containing the double angle, i. e. 2 x, is principally due to causes which
are to be found in the atmosphere or the earth's interior, and which are secondary
effects of the earth'9 position in space. E. J. Wilczynski.
184
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ABSTRACTS AND REVIEWS. r 8 5
GRAY'S TREATISE ON MAGNETISM AND ELECTRICITY. 1
The necessity to the general student of electricity and magnetism, for a
thorough knowledge of the meaning of the so-called " magnetic elements " at
a place, and the best methods for their measurement, has usually caused the
introduction into treatises on the subject, of a more or less complete chapter
on the magnetism of the Earth. In the distinctively mathematical treatises,
such as those of Clerk Maxwell, Mascart and Joubert, Vaschy, or Paul Du-
hem, a brief account is given of Gauss's theory of terrestrial magnetism, and
the methods for the measurement of the " magnetic elements," particularly that
of the horizontal force. In the two former treatises, especially that of Clerk
Maxwell, we have excellent discussions of the theory of all terrestrial mag-
netic measurements.
But Professor Gray, in the work before us, has not only given an account of
the more recent work on the diurnal, annual, and secular changes of the mag-
netic elements, and the possible causes that may be assigned for them, but
he has also added a chapter on the deviations of the compass and the mag-
netism of iron ships, a subject not usually much more than mentioned in
works on electricity and magnetism, save in some of the largest and best
treatises.
Upon the matter of the secular variations, Dr. Bauer's well-known in-
vestigations are quoted, and some of his diagrams are reproduced, both in
the text and among the plates at the end of the volume. There is a short dis-
cussion of the paper of Professor Schuster in the Phil. Trans, for 1889, as to
whether the origin of the diurnal variation is due to causes external, or inter-
nal to the Earth's surface. Von Bezold's discussion of the same subject is
also summarized, and one plate is devoted to his representations of the diurnal
variations of the horizontal force by means of Airy's vector diagrams.
The author apparently adopts, without any reservation, the ideas of Lord
Kelvin as to the impossibility of the direct magnetic action of either the
Sun or Moon, as great magnets, upon the Earth's magnetism, and quotes his
argument based on the magnetic storm of June 25, 1885, and its accompanying
great changes, to show that if these are attributed to electrical oscillatious on
the Sun, then the electrical activity of the Sun during the storm, which lasted
about eight hours, must have been about 160 X io 14 horse power ; that is,
about 364 times the activity of the total solar radiation, which is estimated at
about 3 X 10* 6 ergs per second."
" The electrical energy thus given out by the Sun, in such a storm, would
supply, if transformed to the electrical vibrations of shorter period concerned
in its ordinary radiation, the whole light and heat radiated during a period
of four months. This, as Lord Kelvin remarks, is conclusive against the
hypothesis that these violent magnetic disturbances are due to direct action
of the Sun."
It has been the writer's privilege for many years to have used Professor
Gray's three volumes on " Absolute Measurements in Elecricity and Magnet-
ism," both in laboratory and class-room, and it is with peculiar pleasure that
»A Treatise on Magnetism and Electricity. By Andrew Gray, IX. D.,
F. R. S., Professor of Physics in the University College of North Wales. In two vol-
umes. Vol. I. Macmillan & Co., London and New York. 1898. Price, $4.50.
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x 86 ABSTRACTS AND REVIEWS.
he^finds the present first volume of Professor Gray's new treatise to include a
large part of the theoretical text of those volumes. This has been entirely
recast, however, (much, if not a//, being entirely rewritten,) printed in
larger and better type, with many important additions, and the whole so
treated as to constitute an entirely new and delightful book. This is espe-
cially true of the parts relating to dynamical, and general electro-magnetic,
theory. In the latter, Heaviside's treatment is adopted, which will greatly
recommend it to the rapidly* increasing number of the admirers of that splen-
did electrician. Besides, more and weightier things of the same sort are
promised in the second volume.
Chapter viii, consisting of 63 pages on Fluid Motion, is what might be
considered an innovation in a treatise on electricity ; but of its great utility
there can be no doubt. Those most familiar with theoretical physics will ad-
mit* that the reasons given by the author, in J 270, p. 212, for the insertion of
so long a chapter on hydro-dynamics are abundantly justified.
The book is singularly free from misprints and inadvertencies, especially
when the number and difficulty of the formulae contained in it are con-
sidered. There is what seems an inadvertence on p. 99, in the 18th line from
the bottom, where it would seem that " compass needle" should read "com-
pass card" We look forward to the second volume with a great deal of
interest. John E. Davies.
University of Wisconsin, November 28, 1898.
COMPARISON OF MAGNETIC INSTRUMENTS.
Moureaux, Th. Comparaison des Appareils Magnitiques de Voyage de UOb-
servatoire du Pare Saint-Maur Avec Ceux de Divers Observatoires Mag-
nHiques Atrangers.
Acting upon a resolution of the Meteorological Conference, convened in
Paris, in 1896, to the effect that the comparison of the magnetic surveys of dif-
ferent countries necessitates that the instruments that have been employed in
the different surveys should be compared, M. Moureaux repaired to London and
to Brussels, during the summer of 1897, to compare the portable instruments
used in measuring the magnetic elements in the magnetic survey of France
with those used in determining absolute values in the Magnetic Observatories
of England and Belgium. In the preceding year he had made a like compari-
son with the instruments in the Russian Magnetic Observatory at St Peters-
burg, and Lieutenant Kesslitz, of the Austrian Navy, had come to France to
compare the instruments of the Hydrographic Bureau at Pola with those of
the Pare Saint-Maur Observatory.
Some years before Dr. van Rijckevorsel had made series of observations
at the French Magnetic Observatory at Pare Saint-Maur with instruments
brought from Rotterdam, and likewise Solander had made a comparison be-
tween Stockholm and Pare Saint-Maur. In the meantime an exhaustive dis-
cussion of the intrumental constants of the French instruments led to the de-
duction of a formula for computing the horizontal intensity which gave
values 0.00067 of a C. G. S. unit less than those previously deduced and pub-
lished. In the following tabular statement of all the comparisons that have
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ABSTRACTS AND REVIEWS.
187
been made of the instruments of neighboring countries with those of France,
the differences in the values of the horizontal intensities assigned by van
Rijckevorsel and Solaoder are reduced by 0.00067 :
Name of
Station
Year
of
Mean values of
the observed differences
compared
with
Horizontal
Pare St. Maur
Comparison
Declination
intensity
(C. G. S. units)
Inclination
Kew
1897
-o'.S
-f O.OOOI2
-^.O
Pavlovsk
1896
+i-3
— O.OOOI3
—0.8
Pola
Rotterdam
Stockholm
Uccle
1896
1889
1891
—2.4
+1.1
+0.00006
-j-O.00004
— O.OOO27
—I 5
-5.6
(Brussels)
1897
—1-5
— 0.00002
Van Rijckevorsel. Comparison of the Instruments for Absolute Magnetic
Measurements at Different Observatories. Amsterdam, 1890.
In the spring of 1897, Dr. van Rijckevorsel visited in succession the mag-
netic observatories at Kew, Wilhelmshaven, Potsdam, and Utrecht, carrying
with him to each place a Kew unifilar magnetometer and a standard dip-
circle, with which he made series of observations of the magnetic declination,
horizontal intensity, and inclination, to be compared with simultaneous values
of these elements as deduced for the readings of the standard instruments
of each of the observatories. In 1889 he had obtained comparative sets of
observations, at some of these stations, with the same instruments and in
the same manner. The mean values of the differences between the readings
by his instruments and the instruments for the observation of absolute values
at the observatories are as follows :
Kew
1897 + C.46
1889 + 2^.82
Wilhelmshaven
Declination
+2'.43
+1 .22
Potsdam
+C/.35
Horizontal Intensity (C. G. S. units)
*897 + C/.000108 — o / .oooo23 — o / .oooo92
1889 + C/.000080 -H/.000425 —
i897
1889
+i'.3Q
Inclination
.16
+2 , .6 5
Utrecht
42
,84
-3'.78
-C.85
The conclusions are : (1) That all the declination instruments have prob-
ably undergone slight changes, which may, in some cases, have amounted to
as much as 2 / , or even a little more.
(2) That the differences between the instruments for the observation of
horizontal intensity do not seem to be a constant quantity.
(3) That readings from the dip-circles of the best makers show differ-
ences of as much as 6', and these differences do not seem to be constant.
G. W. LlTTI,EHALBS.
8
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^8 ABSTRACTS AND REVIEWS.
ISOGONIC CHART OF THE UNITED STATES FOR EPOCH 190a 1
In two official publications the same purpose — the construction of the
isogonic chart for the United States, epoch 1900 — is carried out by two differ-
ent departments of the United States Government To which of the charts
shall the outsider give preference ? The first is constructed by a man hith-
erto unknown in the science of terrestrial magnetism ; the second, by one
with nearly half a century of experience in this special field. Again, the first
is issued from a department not engaged in the making of magnetic observa-
tions, while the other comes from a department which for over fifty years has
been actively engaged in magnetic work, and which is intrusted with the car-
rying out of the magnetic survey of the United States. With this statement
of the facts we pass over to a critical examination of each publication.
Geological Survey Publication. Mr. Gannett states that this docu-
ment "is designed to meet the needs of those who have occasion to use the
needle in surveying, or who have to deal with surveys which have been run
by needle in past times." This is the identical purpose of the magnetic work
of the Coast and Geodetic Survey. In no other country has such a thorough
study been made of the secular variation as that by Mr. Schott for the United
States. Mr. Gannett must, therefore, base his secular variation data chiefly
upon the Coast Survey investigations The principal reason apparent to an
outsider for Mr. Gannett's work would be the fact that his isogonic chart is
based upon about 22,000 declination results, while Mr. Schott's is based
upon only about 3,600. Mr. Gannett's additional data are obtained mostly
from the surveys of the United States General Land Office. These, it is
claimed, Mr. Schott has overlooked. This additional material, as Mr. Gan-
nett acknowledges, must be very carefully sifted. It is obtained, not from
observations made by special observers provided with special instruments, but
from the results of surveyors' compass readings. Experience has shown that,
from one cause or another, such results can not, in general, be depended upon
in this country to closer than ^ or i°. The 20,000 observations which Mr.
Gannett obtained thus are liable to an error of the stated amount, while the
3,600 used by Mr. Schott are very largely those made by experienced observers.
It is noticed that where Mr. Gannett has an opportunity of comparing the land-
office data with good determinations — e. g., in the State of Missouri — he is
convinced of their poor quality, and accordingly rejects them. (See p. 213.)
Just how much use should be made of an uncertain mass of data in regions
where good observations are few, can only be safely judged by one who has
the total material before him, and who has obtained the necessary feeling in
the matter from a large amount of experience, both in observation and discus-
sion. No other observational work requires more careful judgment for its
utilization to the best advantage.
Pp. 218-300 contain data for the determination of the secular variation.
The Coast Survey is credited with all the thoroughly reliable data. In ad-
dition the author uses the " data furnished by county surveyors, consisting in
1 United States Geological Survey. Magnetic Declination in the United
Slates, by Henry Gannett. Extract from Part I of the 17th Annual Report of the
Survey, 1895-96. Washington. 1896. Pp. 203-440. Two plates and three figures.
United States Coast and Geodetic Survey. Distribution of the Magnetic
Declination in the United States for the Epoch, fanuary 1, 1900, by Charles A.
Schott. App. 1, Report for 1896. Washington. 1897. Pp. 147-235. Three plates.
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ABSTRACTS AND REVIEWS.
189
the results of experience derived from re-running old lines at different
dates," and the Land Office data. There is apparent here a laudable desire
on the part of the author to make his data as exhaustive as possible. In the
fall of 1895 he sent out a circular to all the county surveyors in the country,
requesting their co-operation, and in response received 850 replies.
The author finally reduces his data to the epoch 1900, and presents the
results in tabular form. The States are arranged alphabetically, and the same
arrangement is followed for the counties and towns in each State. For every
county some result is given, either as obtained from a combination of all the
observations in the county or as estimated from adjoining counties. As a
compilation, this part of Mr. Gannett's work is worthy of praise. But by
making things so easy for the surveyor, has he not really defeated the prac-
tical object of his publication ? The surveyor must not be led to believe that
he can adopt a mean county result for referring his land surveys to the true
meridian. The elimination of local or regional effects by a combination of
many observations into a mean, can have no practical value. Such a mean
result may be out fro:n the true value, for any point within the county, )4°,
i°, and even more at times.
The Coast and Geodetic Survey Publication. The magnetician, com-
paring this publication with the one just discussed, would have no difficulty
in deciding which of the two has the greater scientific value. Mr. Schott
makes use of about 3,600 carefully-selected observations. The best material,
up to the date of the writing of the paper (October 17, 1896), appears to have
been used, with the exception of the results of the detailed magnetic survey
of Maryland, which were published after the construction of the chart. As
Mr. Schott's methods are quite generally known, it will not be necessary to
go into detail with regard to them. We therefore proceed at once to a com-
parative study of the respective isogonic charts.
The two charts, which are on the same scale, 1:7000000, exhibit a great
similarity. The striking thing, however, is that, although Mr. Gannett pro-
fesses to have used nearly 18,000 more observations than Mr. Schott, his iso-
gonic lines do not in general show any more sinuosities— in some cases, not so
many — as Mr. Schott's curves. This circumstance seems strange ; for it has
been repeatedly found that the sinuosities decidedly increase with the multi-
plicity of the observations. We fail to see what internal evidence Mr. Gan-
nett has presented that his chart should be considered superior to the o.ne of
the Coast Survey. The large probable error of the greater mass of his ma-
terial prevented him from recognizing, without question, a regional disturb-
ance. The following table will give some idea of the great similarity of the
two charts :
Values of the Magnetic Declination as Scaled at Points along Parallel of
Latitude 39 .
Longitude
Geol. S.
Coast S.
Diff.
Longitude
Geol. S.
Coast S.
Diff.
W. ofGr.
Chart
Chart
W. ofGr.
Chart
Chart
75°
6°.25W
6°.4 W
— o°.i5
99°
IO°.8
IO°.7
— o°.io
79
3-3
3.25W
4- .05
103
12.6
12 .6
O .OO
P
0.55W
0.3 E
2.8 E
+0.85
107
14.05
14.3
15.85
+O.25
87
295E
—0.15
Hi
15.5
+0.35
9i
575
5 -75
.00
115
16.35
16.8
16. 1
—O .25
95
8.6
8.4
— .20
119
16.6
—O .20
123
17.3 E
I7.75E
+O.45
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I9 o ABSTRACTS AND REVIEWS.
FACSIMILE REPRINTS OF RARE WORKS IN TERRESTRIAL MAG-
NETISM AND METEOROLOGY. 1
He who wishes to intelligently criticise present publications in terrestrial
magnetism should, first of all, familiarize himself thoroughly with the work
of the earlier magneticians. In the absence, however, of a comprehensive
modern treatise on the subject, and owing to the impossibility of procuring,
even in the best libraries, the original publications, this, for most of us, is
impossible.
We therefore welcome, with peculiar gratification, the attempt made by
Professor Hellmann and the Deutsche Meteorologische Gesellschaft to make it
possible for each one of us to possess, in the form of well- executed facsimile
reprints, the most important of the early magnetic publications. As an-
nounced, the reprints embrace rare works, both in meteorology and terrestrial
magnetism. Thus far, eleven numbers have been issued, of which the follow-
ing are of special interest to the magnetician :
No. 4. E. Halley, W. Whiston, J. C. Wilckb, A. v. Humboldt, C. Hansteen :
Die altesten Karten der Isogonen, Isoklinen, Isodynamen. 1701 bis 1826.
25 S. Einleitung u. 7 Karten in Lichtdruck auf 5 Tafeln. Price, 5 Marks.
No. 9. Henry Gellibrand : A Discourse Mathematical on the Variation
of the Magneticall Needle London, 1635. 7 S. Einleitung u. 24 S. Facsimile.
Price, 3 Marks.
No. 10. RARA MAGNETICA. 1269-1599. P. De Maricourt, F. Falero, P.
Nunes, J. De Castro, G. Hartman, M. Cortes, G. Mercator, R. Norman, W.
Borough, S. Stevin. 25 S. Einleitung und 154 S. Neudruck in Facsimile und
Typendruck. Price, 15 Marks.
No. 11. J. H. Winkler, B. Franklin, J. F. Dalibard, L. G. I*e Monnier:
Ubber Luftelektricitat. 1 746-1 755. 8 S. Einleitung und 42 S. Neudruck.
Price, 3-50 Marks.
No. 4 contains a collection of the earliest magnetic charts, while No. 9
gives the earliest indisputable proof of the secular variation. To these two
interesting and valuable reproductions, Numbers 10 and 11 have been added
during the present year, of which the former contains the most important
magnetic publications before the appearance of Gilbert's great work, and the
latter reproduces the first fundamental papers on atmospheric electricity.
We regret that we can not at present enter into fuller detail regarding
these numbers. It will suffice, however, for the magnetician to have before
him the bare contents of No. 10 to be convinced of the veritable treasure-mine
this number contains, viz. : 19 pages of introductory notes by the editor ;
then, facsimile reproductions of the following rarest of publications :
Petrus Peregrin us de Maricourt, De Magnete (1269; Francisco Falero,
Del Nordestear de la Agujas (1535) ; Pedro Nunes, Estromento de Sombras (1537) ;
Joao de Castro, Observac6es Magneticas (1538-1541); Georg Hartmann, Nei-
gung der Magnetnadel (1544); Gerhard Mercator, De Ratione Magnetis circa
Navigationem(i546); Martin Cortes, De la Piedra Yman (1551); Robert Nor-
man, The Newe Attractiue (1531) ; William Borough, A Di scours of the Variation
(1581); Simon Stevin, De Havenvinding (1599). L. A. B.
iNeudrucke von Schriften und Karten uber METEOROLOGIE UND
ERDMAGNETISMUS, Herausgegeben von Professor Dr. G. Hsllmann.
A. Ascher & Co., Berlin.
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ABSTRACTS AND REVIEWS.
191
CONTRIBUTIONS TO THE THEORY OF THE EARTH'S MAGNETISM.
Von Bkzoud, W. Zur Theorie des Erdtnagnetismus. Sitzber. d. Akad. d. Wiss.
zu Berlin, 1897. XVIII. 36 pp. and 2 plates.
This paper, presented to the Berlin Academy on April 1, 1897, consists of
two parts. The first deals with the fundamental principles of Gauss's poten-
tial theory of the Earth's magnetism, especially with reference to the experi-
mental verification of the assumption of a potential. For this purpose the
author takes the line integral of the force along certain parallels of latitude,
as based upon Schmidt's data. This line integral should, of course, vanish
in case the entire force is due to a potential. As a matter of fact, however,
these quantities were found to be :
For latitude, . . . 50 N. 45 N. 40 N. Equator
cos JY d A 0.00389 0.00652 0.00699 —0.00859
Range of potential 0.072 0.081 0.087 0.138
To obtain some idea of the magnitude of the deviations of the line in-
tegral values from zero, von Bezold compared them to the range of potential
(difference between extreme values) along the same parallel, and found that
for the very region of the Earth in which the observations are most numer-
ous, the ratio of the integral value to the potential range is largest — viz.,
8 per cent— while along the equator, where the observations are not so fre-
quent, the ratio is hardly 1 per cent It would seem, then, that it can not be
said offhand that the deviations of the line integral values from zero are to
be referred entirely to insufficient or inaccurate data. Attention might be
called to the systematic variation in the values with latitude; which fact,
however, is more clearly exhibited in a paper presented before the Washing-
tan Philosophical Society, on January 9, 1897. (See T. Af. t Vol. II, p. 11.)
The author, furthermore, examines the potential hypothesis for small re-
gions, and, like Riicker and Carlheim-Gyllenskold, finds that the closing er-
rors of the line integral are of the order of the observation errors.
The second part of the paper, dealing with the diurnal variation, can not
be done justice to in the short space remaining to us. We therefore post-
pone its discussion, and that of a related paper by Liideling, to the next num-
ber of the Journal. L. A. B.
CHANGE OF MAGNETIC ELEMENTS WITH ALTITUDE.
Liznar, J. Ucber die Aenderung der erdmagnetischen Kraft mit der Hohe.
Sitzungsber. d. kais. Akad. d. Wiss. in Wien. Math, naturw. Classe, Bd.
C VII, Abth. II- Juni, 1898.
If h is the altitude above the sea-level, and //]*, 7X, Dh> h denote the hor-
izontal intensity, total intensity, declination and inclination, respectively, at
the altitude h, ff ot etc., the same quantities for h=o, it is found, with the aid
of the Gaussian potential theory, that the differences Hh — /f =Sf/h t etc., are:
where R is the Earth's radius. In these formulae h 1 , and higher powers, are
neglected. If the north and west components are denoted by X and Y> and
the vertical component by Z.
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1 92 ABSTRACTS AND RE VIE WS.
In order to compare these values with the observations, Professor Liznar
uses the results of the Austrian magnetic survey for 1890. He divides the
observations into three groups of 77, 72, and 56 different stations, according to
altitude. He finds that the west component, as well as the declination, in-
creases with the altitude, instead of decreasing- as prescribed by above for-
mulae. The other elements, however, decrease^ but three times as rapidly as
the formula requires. He concludes that this proves the existence of extra-
terrestrial magnetic influences directed south, west, and upward. The author
thinks that these are the same forces which cause the observed variations,
and urges the importance of mountain stations from this standpoint. For at
different elevations, if this idea is correct, the amplitude of the variations
should be different. Finally the author shows how to correct magnetic ob-
servations for altitude, making use of the previous results.
E. J. Wilczynskl
RECENT PUBLICATIONS
Arent, Th. Die Theorie des Polarlichtes von Adam Paulsen. Repr. from
"Das Wetter," Heft 3, 1897. P. 10.
[Gives an account of Paulsen's theory ; c. f. T. M. Vol. I. Pp. 159.]
Bigelow, F. H. Comments on Bulletin 21. "Solar and Terrestrial Magnet-
ism in their Relations to Meteorology. Am. J. of Science, June 1898. Pp
455-462.
[For A. Schuster's review of this paper, see present number of T. M.]
Bombay. Magnetical and Meteorological Observations, made at the Govern-
ment Observatory, Bombay, 1896, under the direction of N. A. F. Moos.
Bombay, 1897.
Folgheraiter, G. La magnetizzazione dell' argilla colla cottura in re-
lazione colle ipotesi sulla fabbricazione del vasellame vero etrusco. Roma,
1897. 8°. Repr. Rendiconti della R. Academia dei Lincei, Die.
1897. Pp. 368-370.
Hepites St. C. Annales de l'lnstitut M£teorologique de Roumanie pour
l'annee 1896. Tome XII. Bucharest, 1898.
[This volume contains nothing pertaining to terrestrial magnetism, with
the exception of a brief article by D. Bungetzianu on the Pawlowsk Ob-
servatory.]
Heydweiller, Adolf. Neue Erdmagnetische Intensitatsvariometer. Repr.
Annalen der Physik und Chemie, Neue Folge, Bd. 64, 1898. Pp. 7.
Liznar, J. Die Vertheilung der erdmagnetischen Kraft in Osterreich-Ungarn
zur Epoche 1890.0 nach den in den Yahren 1889 bis 1894 ausgefiihrten
Messungen. II Theil. Wien, 1898. Pp. 96 and 8 plates.
Potsdam. Ergebnisse der magnetischen Beobachtungen in Potsdam. Ber-
lin, 1897 and '98.
[Five publications of the Prussian Meteorological Institute, Professor
W. von Bezold, director, giving the results of the magnetic observations for
the years 1892, '93, '94, '95, ana '96. A more detailed account will be given in
a future number of T. M.]
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NOTES
The Berlin Academy, at its meeting October 27, 1898, granted Dr. Ad.
Schmidt (Gotha) 2,500 marks to assist him in collecting and discussing recent
magnetic data. This money has been most worthily bestowed.
Magnetic Storm. On the afternoon of November 21, while my students
were making magnetic observations, there were indications of a magnetic
storm. The magnetograph traces of the new Toronto observatory, courteously
furnished by the director, have verified these indications, the maximum dis-
turbance in declination occurring the next morning about 6 a.m. The
peculiar atmospheric conditions at the time warrant a careful study of the
storm. L. A. B.
SECULAR MOTION OF A FREE MAGNETIC NEEDLE.
In a recent publication, 1 my friend, Mr. Littlehales, has continued, and ex-
tended to other parts of the earth, the investigation, begun by me in 1892, of
the curves described, in the lapse of time, by the north end of a freely-sus-
pended magnetic needle. He follows precisely the same methods, and like-
wise exhibits on a chart of the earth, 122 x 68 cm., the various secular motion
curves, supposing length of needle two feet, in the true geographical position
of the stations. The author has already given in the Journal some account
of his secular variation investigations.' (Vol. I, pp. 62 and 89; II, p. 68.)
Thirty stations are discussed, of which those marked with an asterisk I
had already investigated, viz. : Arica, Ascension Island * Bahia, Barbadoes,
Batavia, Bombay, Callao, Cape of Good Hope,* City of Mexico, Concepcion,
Coquimbo, Fayal (Azores),* Habana, Hongkong, Honolulu, Magdalena Bay,
Manila,* Montevideo, Paita, Panama, Pernambuco, Petrapavlovsk,* Punta Are-
nas, Rio de Janeiro,* St. Helena,* Shanghai, Singapore, Sydney, Tahiti, and
Valparaiso.
The direction of motion of the north end of the needle, as viewed from
the point of suspension is, in general, clockwise. There are, however, some
stations in the Pacific Ocean, and on both its shores, which exhibit at present
either no decided direction or a reversal, in part, of the general motion. Mr.
Schott, likewise, found similar indications at certain stations on the west coast
of North America. (See Terrestrial Magnetism, Vol. II, p. 39.) I may be per-
mitted to point out that evidence of deviations from the clockwise direction had
already been furnished by my own investigations. I quote the following from
page 50 of my Ph. D. thesis : " Fur diesen Erdtheil [6o° E— 200 E] scheinen
die Sacular-Curven iiberbaupt sehr klein zu sein; manchmal sind sie nahezu
gerade Linien, da die Aenderung hauptsachlich bei der Inclination eintritt
(siehe Manila Tafel 1). Diese Thatsache tritt sehr hiibsch hervor in der zu
Capitel III gehorigen Karte. Man konnte fast unzweideutig schliessen, dass
entgegengesetzte Wellen im Stillen Ocean und an dessen Kiiste auftreten."
With the view of systematizing secular variation investigations, I hope to
be able to publish a paper on this subject in a future issue of the Journal
L. A. B.
1 See Terrestrial Magnetism, Vol. II, p. 163.
193
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ANNO UN CEMENT.
With the March, 1899, issue, this Journal, devoted exclusively to Terrestrial Magnetism,
Atmospheric Electricity, and allied subjects— such as Earth Currents, Auroras, etc — enters
on its fourth volume. The hearty co-operation extended, and the warm encouragement re-
ceived from all sides, are the surest proof that the inauguration of this Journal has met a
keenly felt want Doubtless never before has such enthusiastic interest been taken in these
most elusive subjects.
It has been found necessary to enlarge the periodical somewhat, and, in consequence,
there will be a slight increase in the subscription price. Attention is called to the change in
the name and to the valuable assistance the Editors will have in conducting the Journal.
How satisfactorily the purpose of this periodical has been fulfilled in the past can be seen
by looking over the Table of Contents of Volumes I, II, and III. No one who wishes to
keep abreast of the latest and best thought in these comparatively unexplored sciences can
afford to be without this Journal.
Avis! Le numero de Mars, 1899, commence le tome IV de ce journal exclusivement
destin€ au magnetisme terrestre, a V Electricity atmosphenque, et a leurs allies — les courants
terrestres, les aurores, etc L' active collaboration et V encouragement cordial recus de tons
cotes sont preuve sure de ce que ce journal est venu combler une lacune devenue tres-sensible.
Sans doute cette branche delicate des sciences naturelles n* a jamais €t€ l'objet de tant d'in-
teret et d' enthousiasme qu* on y porte de nos jours.
X cause de V accroissement qu HI a fallu donner au journal, on en a legerement augmente
le prix d' abonnement. Veuillez aussi remarquer le changement de titre et le concours dis-
tingue 1 sur lequel pourront compter les redacteurs. Le contenu des trois premiers tomes
montre comment ces pages out su satisfaire a leur t&che. Desormais ceux qui voudraient se
tenir au courant des idees les plus modernes et les plus fee on des sur ces domaines pen ex-
plores jusqu' ici, ne sauraient guere se passer de notre journal.
Zur Beachtung / Mit dem Marzhefte 1899 tritt diese Zeitschrift, welche ausschliesslich
dem Erdmagnetismus, der Luftelectricitat und verwandten Erscheinungen, wie Erdstromun-
gen, Nordlicht u. s. w., gewidmet ist, in ihreu vierten Jahrgang ein. Dass ihr Erscheinen
einem deutlich gefuhlten Bediirfnisse entsprach, beweist die allseitig gewahrte lebhafte
Teilnahme und Mitwirkung der Fachleute. Sicher ist nie zuvor das Interesse an unserem
schwierigen Gegenstande so stark hervorgetreten, wie in unseren Tagen. Eine Vergros-
serung der Zeitschrift ist notig geworden und hat eine geringe Erhohung des Abonnements-
preises mit sich gebracht. Wir weisen noch auf die Veranderung unseres Titelblattes hin,
sowie auf die wertvolle Mithulfe, deren sich die Herausgeber zu erfreuen haben werden. In
wie befriedigender Weise das Journal bisher seinen Zweck erfullt hat, erhellt aus dem In-
haltsverzeichnisse seiner drei ersten Jahrgange. Niemand, der mit den neuesten und her-
vorragendsten Porschungen auf diesen noch verhaltnismassig brach liegenden Gebieten in
Beriihrung bleiben will, kann hinfort unserer Zeitschrift entbehren.
Address: Terrestrial Magnetism, University of Cincinnati, Cincinnati, Ohio.
Foreign Agents : Wesley and Son, London ; Mayer and Miiller, Berlin.
Terrestrial Magnetism and Atmospheric Electricity will appear four times a
year, viz., during the months of March, June, September, and December. A volume will con-
sist of four numbers, embrace about 256 pages, and begin with the March issue.
Communications relating to the subject-matter of the Journal, as broadly defined and
suggested by the title, are solicited. All languages that can be printed with Roman charac-
ters will be admitted. One of the main languages, however, should be used whenever possible.
Publications intended for review should be sent in duplicate, when possible.
The editors can not hold themselves responsible for opinions expressed by contributors.
Authors of original articles will be furnished with fifty reprints, in covers, free of cost,
provided the request accompanies manuscript. Additional copies can be obtained at cost
price.
All correspondence should be addressed:
TERRESTRIAL MAGNETISM, The University of Cincinnati, Cincinnati, Ohio.
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Terrestrial Magnetism
AND
Atmospheric Electricity
An International Quarterly Journal
Conducted by
L. A. BAUER,
Coast and Geodetic Survey, Washington, D. C.
With the Assistance of
M.
ESCHENHAGEN A. SCHUSTER
Potsdam Manchester
TH. MOUREAUX J. ELSTER and H. GEITEL
Pare St. Maur Wolfenbuttel
G.
W. LITTLEHALES A. McADIE
Washington San Francisco
Foreign Councillors
A.
w. rCcker e. mascart
England France
W.
VON BEZOLD M. RYKATCHEW
Germany Russia
American Councillors
T.
C. MENDENHALL C. A. SCHOTT '
Worcester Washington
VOLUME IV
MARCH-DECEMBER, 1899
Published by
THE JOHNS HOPKINS PRESS,
Baltimore, Maryland.
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2<Hki
'EN FOUNDATIONS '
1900. L ' :
1
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CONTRIBUTORS TO VOLUME IV
Cleveland Abbe Washington, District of Columbia
L.A.Bauer Washington, District of Columbia
Mrs. L. A. Bauer Washington, District of Columbia
Charles Chree Richmond, England
J. E. Da VIES Madison, Wisconsin
J. Elster Wolfenbiittel, Germany
M. Eschenhagen Potsdam, Germany
J. A. Fleming Washington, District of Columbia
Thomas French Cincinnati, Ohio
H. Geitel Wolfenbiittel, Germany
W. W. Griffith Columbia, Missouri
J. F. Hayford , Washington, District of Columbia
G. Hellmann . . . .• Berlin, Germany
A. Heydweiller Breslau, Germany
G. W. Littlehales Washington, District of Columbia
G. Ludeling Potsdam, Germany
E. MascarT Paris, France
A. McAdie San Francisco, California
Th. Moureaux Paris, France
L. Palazzo Rome, Italy
A. W. Rucker London, England
Adolf Schmidt Gotha, Germany
H. Stade Brocken, Germany
Alexis db Tillo St Petersburg, Russia
H. W. Vehrenkamp Cincinnati, Ohio
P. Wernicke Lexington, Kentucky
E. Wilczynski Berkeley, California
H. Wild Zurich, Switzerland
v
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TABLE OF CONTENTS
GENERAL
PAGE
AIMANTATION INDUITE PAR LE CHAMP TERRESTRE SUR LES AlMANTS
E. Mascart i
Beobachtungen Ober die EigenelectricitXt der AtmosphXr-
ischen NiederschlXge /. Elster and H. Geitel 15
/ Biographical Sketch and Portrait of Dr. John Locke
L. A, Bauer 133
/ Biographical Sketch of Professor Neumayer 203
Carte Magnetique dr la Sicile L. Palazzo 87
Completes Oberirdisches Magnetisches Observatorium
H. Wild 169
Erdmagnetische Beobachtungen im Umanaks- Fjord (Nordwest
Gronland), 1892-93 H. Stade 62
Is the Principal Source of the Secular Variation of the
Earth's Magnetism Within or Without the Earth's
Crust ? L. A. Bauer ; 53
Is There a Four hundred-and-twenty-eight-day Period in
Terrestrial Magnetism ? J. F. Hay ford 7
Le Cadet's Treatise on Atmospheric Electricity . A. McAdie 145
Mean Values of Magnetic Elements at Magnetic Observa-
tories C. Chree 135
New Magnetic Intensity Variometers ... Adolf Heydweiller 240
Remarks Upon Professor Rucker's Paper and Wilde's Mag-
netarium L. A. Bauer 130
sur la periodicite des perturbations de l'alguille almantee
Horizontals, a l' Observatoire du Parc Saint-Maur
Th. Moureaux 149
Sur la Relation qui existe entre la Repartition des Slements
Magnetiques et la Distribution G6nbrale des mers et
de la Temperature Moyenne Annuelle X la Surface du
Globe A. de Tillo 237
Tafeln zur GenXhertrn Auswertung von Kugelfunctionen
und ihren Differentialquotienten . Ad, Schmidt (Gotha) 59
The Beginnings of Magnetic Observations . . . G. Hellmann 73
The Influence of the Earth upon the Field of a Bar-Magnet
W. W. Griffith 199
The Magnetic Work of the United States Coast and Geo-
detic Survey L. A. Bauer 93
The Physical Decomposition of the Earth's Permanent Mag-
netic Field. — No. 1. The Assumed Normal Magnetiza-
tion and the Characteristics of the Resulting Resid-
ual Field L. A. Bauer 33
The Secondary Magnetic Field of the Earth . A. W. Rucker 1 13
vi
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TABLE OF CONTENTS vii
PAGE
Ueber die Errichtung StationXrer dnd Tempor&rer Mag-
netischer Observatorien M. Eschenhagen 261
Ueber die Existenz Electrischbr Ionen in der Atmospharb
/. Elster and H. Geitel 213
Ueber die TXguche Periode des Erdmagnetismus und der
Erdmagnetischen Storungbn an Poi^arstationbn
G. Ludeling 245
Abstract of Dr. Ludeling's Researches . . L. A. Bauer 260
Ueber einige Problbmb des Erdmagnetismus und die Noth-
wendigkeit einer internationai^n organisation
M. Eschenhagen 105
Ueber die Mogmchkbit, Vou^tandigb Magnetische Observa-
torien Ganz Oberirdisch und in einem Gebaude Einzu-
RICHTEN H. Wild 153
View of Pawlowsk Observatory 272
NOTES
Activity in Magnetic Work 72
Magnetic Work in the United States
Magnetic Survey of Northern Germany
Magnetic Work in the Australasian Colonies
Activity in Magnetic Work 137, 138
Notice to Correspondents
Reprinted Edition of Volume I
Grant from the Smithsonian Institution to the Journal
Comparison of Instruments made by Prof. M. Eschenhagen
Appointment of Prof. Joseph Lizuar to the Professorship of
Meteorology at the University of Vienna
Division of Terrestrial Magnetism of the United States Coast
and Geodetic Survey
Magnetic Observatory at Vienna
Batavia Magnetic Observatory, Java
Magnetic Effect from Electric Tramways
Magnetic Observatory at Pola
Magnetic Survey of North Carolina by Mr. James B. Baylor
Magnetic Survey of Maryland
Instruction in Terrestrial Magnetism at the Massachusetts In-
stitute of Technology, Boston, Mass.
Activity in Magnetic Work 204, 205
Notice to Workers in the Fields of Terrestrial Magnetism and
Atmospheric Electricity
Professor W. von Bezold's paper at the meeting of the Berlin
Academy, June 15th.
Comparisons made by Dr. van Rijckevorsel
Magnetic Work of Dr. Edler of Potsdam
Professor Birkeland's expedition to Bossekop
Professor Adam Paulsen's proposed trip to Iceland
Signor Rajna's article entitled " La trazione 'elettrica e gli
osservatorii magnetici"
Appointment of Professor A. McAdie as Honorary Lecturer on
Meteorology at the University of California
h. A. Bauer's visit to European Magnetic Observatories
Appointments in Division of Terrestrial Magnetism
Coast Survey
Magnetic Observations in Alaska by Messrs. Putnam, Farris,
and Ritter
Notes on Current Work in Terrestrial Magnetism, etc. . . 274-276
/ Biographical Sketch of Professor Rucker 71
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viii TABLE OF COXTENTS
PAGE
/ Biographical Sketch of Charles A. Schott 136
' Biographical Sketch of Professor Neumayer 203
/ Biographical Scetch of Professor Wild 273
ABSTRACTS AND REVIEWS
Boller, W. : Das Siidlicht C. Abbe 207
BoRGEN, C: Zur Lehre von der Deviation des Kompasses. Ablei-
tung des Ausdrucks fiir die Schwingnngsdauer einer nnter
dem Einflusse eines beliebig gelegenen Magnets stefaenden
Nadel J. E. Davits 67
Cicera, R. : El Magnetisino Terrestre en Pilipinas . Thomas French 139
Folgheraiter, L. : Magnetic Effects produced by Lightning
" Nature " 209
Lemstrom, S.: Experiments on the Influence of Electricity on Grow-
ing Vegetables or Plants J. A. Fleming 207
Lemstrom and Biese. : Observations faites aux stations de Sodan-
kylk et de Kultala. felectricit£ atmosph£rique, courants tel-
luriques, courant 61ectrique de Patmosphere, ph£nomenes lu-
mineux de P aurore bore"ale, naturels et artificiels . A. Mr A die 65
Louis, David A. : The Great Magnetite Deposits of Swedish Lap-
land J. A. Fleming 276
Marini : Disturbing Effects of Electric Tramways on Magnetic
Needles *• The Electrical World and Engineer" 209
Moureaux, Th. : Determinations Faites dans le Gouvernement de
Koursk (Russie) en 1896, Par M. Th. Moureaux
G. W. Littlehales 235
Niesten, L. : Bulletin mensuel du magne'tistne terrestre de P Obser-
vatoire Royal de Belgique L. A. Bauer 209
Nippoldt, A., Jr. : Ein Verfahren zur harmonischen Analyse erd-
magnetischer Beob*achtungen nach einheitlichem Plane
E.J, Wilczynski 141
Recent Papers on Atmospheric Electricity
Naturwiss. Rundschau
Bensdorf, H.: Measurements of Falls of Potential in Siberia 207
Thuma, J. : Measurements of Atmospheric Electricity in a
Balloon 208
Ludwig, R. : On the Measurements of Atmospheric Electricity
made during the total eclipse of the Sun, Jan. 22, 1898 . . 208
Semmola : Atmospheric Potential 207
Trabert, H. : Der Zusammenhaug zwischen den Erscheinungen des
Erdmagnetismus und den elektrischen Vorgangen in der At-
mosphare H. Geitel 63
Wild, H. : TTeber die Errichtung erdmagnetischer Observatorien
M. Eschenhagen 69
Ueber die Bestimmung der erdmagnetischen Inclination und
ihrer Variationen M. Eschenhagen 142
Ueber die Differenz der mit einem CJnifilar-Theodolith und
einem Bifilar-Theodolith bestimmten Horizontal -In ten si-
taten des Erdmagnetismus Af. Eschenhagen 143
PUBLICATIONS
Recent Publications 144, 210-212
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(Plate I.I
^^^CTfc $^6^
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Terrestrial Magnetism
and
Atmospheric Electricity
VOLUME IV
MARCH, 1899
Number i
AIMANTATION INDUITE PAR LE CHAMP TERRESTRE
SUR LES AIMANTS.
Par M. E. Mascart.
Dans la m6thode de Gauss, g6n6ralement employee pour 6valuer
la composante horizontale H du champ terrestre, on determine
d'abord le produit P = Afffdu moment magnetique Afd'un barreau
par cette composante, k Taide des oscillations, puis le quotient
M
Q = -zy an moyen des deviations que le barreau produit sur un
d6clinom&tre.
Dans ces experiences, le moment magnetique du barreau est
modifie par Taimantation induite que produit le champ terrestre ;
on est d'ailleurs autoris6 k admettre que cette aimantation est uni-
quement temporaire, reversible sans hysteresis, et proportionnelle
au champ.
Pour les oscillations, par exemple, si Ton appelle A Taiman-
tation rigide du barreau, / et m les coefficients moyens d'aiman-
tation longitudinale et transversale, et a Tangle du barreau avec
le meridien magnetique, l'aimantation totale a une composante
longitudinale A + iff cos a
et une composante transversale
mH sin a.
En designant pat v le volume du barreau, le couple produit par le
champ terrestre est alors
C= v(A + IH cos a) If sin a — vmH s\n a. H cos a
ou, en remarquant que le moment magnetique rigide est M=vA ,
/ — m
= mh(
1 +
a 1 sir
H cos a ) sin a
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2 E. MASCART [vol. iv, no. i )
Lorsque les deviations sont trfes petites, ce qui est le cas des
oscillations, on peut remplacer cos a par l'unite, de sorte que l'ex-
p^rience donne, en realite, le produit
P , = Af//^i + i -^ /A=P(i +x) .
Difterentes m^thodes ont €t6 propos^es pour determiner le terme
de correction x qu'il convient d'apporter aux observations pour en
d^duire le produit P.
Lamont fait agir sur son declinom&tre l'un des pdles du barreau
place verticalement, dans le sens direct et dans le sens inverse;
Taimantation induite par la composante verticale s'ajoute dans un
cas a l'aimantation rigide et s'en retrancbe dans l'autre. La diffe-
rence des deviations, toutes corrections faites des defauts de sy-
metrie, donne la demi-somme des aimantations longitudinales, di-
recte et inverse, sans les separer Tune de l'autre ; la solution du
probl&me est done incomplete et on n'a pas l'aimantation trans-
versale.
Joule se sert de deux barreaux aussi identiques que possible,
qu'il fait osciller d'abord separement et qu'il monte ensuite sur un
equipage commun, de manure que le cbamp de Tun sur l'autre soit
a peu prfes egal au champ terrestre. La derni£re experience serait
debarrassee des aimantations induites et la comparaison du resultat
avec les deux premieres determinerait la valeur de x. On doit alors
faire intervenir trois moments d'inertie et on n'en deduit encore
que le coefficient d'aimantation longitudinale. 1
Je n'ai pas connaissance qu'on ait indiqu<§ d'autre metbode, a
part celle qui consisterait a mesurer le produit P = M H en ame-
nant le barreau par une suspension bifilaire dans la direction trans-
versale au meridien magnetique.
La question est si importante pour les etudes de magnetisme
terrestre qu'il m'a paru utile de chercher des procedes plus prati-
ques et plus directs.
i° Supposons qu'on place un barreau aimante M suivant l'axe
d'une bobine cylindrique assez longue pour que le champ d'un
courant qui parcourrait le fil soit a peu pr&s uniforme dans la re-
gion occupee par l'aimant. Si n est le nombre de spires par unite
de longueur, le flux de force emis dans le circuit par l'aimant est
4 7T « M. Si m£me la bobine n'est pas assez longue pour qu'on
puisse negliger Taction des bases, ce flux reste proportionnel a jf/et
peut £tre represente par p Af, pourvu que le barreau occupe chaque
fois la m£me position.
1 Mascart et Joubert. Lemons sur l'e'lectricite' et le magnetisme. 2© Edition,
Tome II, page 734J 1897.
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AIMANTATION INDUITE SUR LES AIMANTS 3
L'axe de la bobine £tant d'abord horizontal et parallele au m€-
ridien magn&ique, et le barreau dans la position directe, auquel cas
son aimantation est A + Iff, le flux de force qu'il.e'met dans la bo-
(l j-i\
1 + —r J. En meme temps, si 5 est la surface de
l'ensemble des spires, le flux de force total est
Quand on tourne le systeme de 90 autour d'un axe vertical, le
flux de force n'est plus que
<f>'=pAf.
On relie la bobine k un galvanometre balistique par un circuit
de resistance R. La de*charge induite q pendant la rotation est
L FT
Rq = ^ — 4,'=pM ~ + HS.
A
Pour e'liminer l'induction par le champ terrestre, on r6pete la
m£me observation ct blanc, c'est-a-dire sans aimant, ce qui donne:
Rq» = HS,
Le systeme 6tant k 90 du meVidien, on donne au circuit une
resistance plus grande R\ afin de rendre les d£charges comparables,
et on enieve l'aimant. La nouvelle d6charge q' est alors:
R'q' = <t>' = pM.
En appelant a, a et a les angles d'impulsion du galvanometre,
corrig£s de Tamortissement, qui correspondent k ces diffSrentes d€-
charges, on en d6duit:
A ~ R 7 !? ~ R' ' a' '
L'exp^rience est rapide et tres simple; elle n'exige d'autre me-
sure que celle du raport des angles d'impulsion et du rapport des
resistances. On determine ainsi le coefficient moyen / d'aimantation
longitudinale dans le sens direct.
Partant de la direction 06 le systeme est perpendiculaire au m€-
ridien, si on tourne encore de 90 , de maniere que Taimant occupe
la position inverse, auquel cas le coefficient d'aimantation induite
est /' , le nouveau flux de force devient
et la decharge
Rq"=<j>'—<j>" = pM l -^+HS.
A
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4 E. MASCART [Vol. iv, no. i.)
L'angle d'impulsion correspondant a" donne alors
RW-q!>=pM 1 ^,
VH_R qr — q, _R a" — %
A —R'- J —R" a' •
2° Pour determiner l'aimantation transversale, on porte l'aimant
par une suspension bifilaire, de coefficient C, au milieu d'un syst&me
de cadres galvanom&riques capable de produire un champ sen-
siblement uniforme H' , de m£me ordre que le champ terrestre.
L'axe de ce systfeme 6tant suppose perpendiculaire au m6ridien
magn&ique, on amfene l'aimant dans la position transverse par une
torsion convenable 6 du bifilaire ; la condition d'6quilibre est
(i) HM=C sin 6 .
On fait alors passer le courant qui produit le champ auxiliaire
H' dans le sens de l'aimantation primitive. Le moment magn£-
tique du barreau est augment^, Taction du champ terrestre devient
plus grande et il se produit une deviation 8.
Dans cette situation, les composantes longitudinale et transver-
sale du champ total sur le barreau sont
//'cos8 + ^sin8 et ZfcosS — /T sin 8
et les aimantations correspondantes
/*,=/(//' cos 8 + ^7 sin 8) , A, = m (//cos 8 — //'sin 8) .
Le champ terrestre et le champ auxiliaire produisent des couples
de sens contraires qui sont :
//;*/[( i + 4) CO s8 — ^sin8],
^'J/[(i + 4)sin8 + 4 CO s8].
A A
Comme les quotients -j et -j sont trfes petits, ainsi que la d£-
viation 8, on pourra ndgliger les termes du second ordre. D'autre
part, le couple de torsion est devenu C sin (6 + 8), et la condition
d'6quilibre est
^ I + ^ / j«^'^|8 i .^i = Csin(e + 8) = Csin^+8.Ccosfl.
Tenant compte de liquation primitive (i), il en r£sulte:
^'^/{=^// = 8(Ccos^ + ^ , iV)=^'iV(i+^cotg^)s,
^/y=*=(i + ^,cotg*)8.
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AIMANTATION INDUITE SUR LES AIMANTS 5
On obtient ainsi directement le terme de correction x qu'il
convient d'apporter aux experiences d'oscillations.
La deviation 8 se mesure trfes exactement par la m£thode du mi-
roir ; on lvalue le rapport des champs H et H' en ramenant Taxe
du galvanomfetre dans le m6ridien et faisant osciller une mfeme
aiguille sous Tinfluence des champs H et H -\- H* \ enfin, il n'est
pas n£cessaire de connaltre Tangle $ avec une grande approxima-
tion. On peut remarquer m£me que si le bifilaire est r6g\€ de fagon
que $ = 90 , il reste simplement x = 8.
On a suppos6 toutefois des conditions difficiles a r£aliser en
toute rigueur et il est n6cessaire d'examiner Tinfluence des erreurs
de r£glage.
Soient a et c les angles, supposes trfes petits, que fait Taxe mag-
n6tique du barreau avec la normale au m£ridien et avec la direction
du champ H' dans la premiere experience.
Aux termes du second ordre prfes, Tangle a n'intervient pas et
liquation (1) reste exacte. Quand on fait agir le champ auxiliaire,
les aimantations induites, longitudinale et transversale, peuvent
encore 1 se r^duire a
A X =IH' et A t = m/f;
le couple dii au champ terrestre est
i/if/(i + ^)cos(8 + c) = //^(i+^)
et celui du champ auxiliaire
La condition d'6quiJibre est done:
Hm[i + 1 ^-} — H' mU+ € + ^\= Csm$ + h . CqosB ,
ou, en tenant compte de (1),
I—nt rr i , If
Jf=x=(i + ^,cotg$ ) j$+€.
Comme la quantity x est de Tordre des milli&mes, il faut que
Terreur e soit beaucoup plus faible, e'est-a-dire infiSrieure a i\ qui
vaut 0.0003.
La precaution importante est done que le champ auxiliaire H'
reste parallfele a Taxe magndtique du barreau dans la position
transverse.
Nous avons employ^, pour produire ce champ, la bobine de Von
Helmholtz k deux cadres circulaires s6par6s par une distance £gale
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6 E. MASCART [Vol. iv, no. i]
a leur rayon. I/appareil porte un prisme, a faces rectangulaires
argent6es, dont une des faces peut §tre placee dans le m£me plan
que le miroir mobile suspendu a l'6trier du barreau. Le treuil a
cercle divis6 du bifilaire est monte sur une traverse qui s'appuie sur
les deux cadres.
On am&ne d'abord l'axe de la bobine dans le m6ridien, le bifilaire
£tant sans torsion, de sorte que Taxe magndtique du barreau soit
lui-m&me dans le m6ridien ; ces diff£rentes conditions ne sont reali-
ses que d'une mani&re approch6e. Quand on fait passer le cou-
rant producteur du champ H\ la deviation du barreau doit £tre
rigoureusement nulle si le champ est parallele a Taxe magnetique.
Une premiere lunette L, qui vise a la fois les images d'une £chelle
dans le prisme et le miroir mobile, permet de verifier quand la con-
dition est remplie. On note alors le nombre n de divisions dont une
image chevauche sur Tautre, ce qui correspond a Tangle fi des deux
miroirs. On tourne ensuite le cadre de 90 , par Tobservation de la
lunette sur la seconde face du prisme.
Une seconde lunette U est install£e a angle droit de la premiere;
elle vise ainsi Timage de son dchelle sur la premiere face du prisme
dans sa nouvelle position.
II suflit maintenant de tordre le bifilaire jusqu'a ce que Tangle
du miroir mobile avec cette face reprenne la valeur primitive fi. Le
d£placement relatif des images est encore de n divisions si les echelles
ont 6t€ instances a la m£me distance.
L'appareil est ainsi r£gle et la torsion du tambour donne Tangle
0. La lunette U permet ensuite d'£valuer la deviation 8 que pro-
duit le champ H\
La premiere methode donne a = - , la seconde x = -
A A
m FT
et la difference a — x = — — . On a done s£par6ment les deux
quantity qui interviennent dans la determination du produit P=MH
par les oscillations.
Quand on mesure le quotient Q par la methode des tangentes,
les corrections relatives a Taimantation induite sur le barreau de-
viant et sur le d£clinometre sont n6gligeables, mais ces corrections
interviennent partiellement dans la mdthode des sinus, Je sortirais
de mon cadre en discutant cette question.
Sans reproduire ici les valeurs obtenues par M. Moureaux, au
Pare Saint-Maur, il me suffira d'ajouter que la mesure des aimanta-
tions induites est relativement facile et que les r6sultats pr6sentent
une grande concordance.
6 Janv. 1899.
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IS THERE A 428-DAY PERIOD IN TERRESTRIAL
MAGNETISM?
By John F. Hayford, Expert Computer and Geodesist, United States
Coast and Geodetic Survey.
That terrestrial latitudes vary with an average period of 428
days seems now to be an established fact. In other words, the pole
of figure of the Earth is known to be moving continuously around
its pole of rotation in the direction of decreasing west longitudes at
a mean rate of one complete circuit in 428 days (ignoring for our
present purpose the corresponding annual motion of the pole of
figure). For each position of the pole of figure a set of stresses
must be produced in the Earth representing its tendency to assume
a new figure, — a new ellipsoid of revolution with its axis of figure
coincident with the axis of revolution. These stresses are doubt-
less partially relieved, and only partially, by actual movements of
matter to new positions in the oceans, in the envelope of atmos-
phere, and perhaps in the so-called rigid Earth. Even with this
partial relief each portion of the Earth is subjected to periodic
stresses which repeat their various phases every 428 days. This
suggests that there may possibly be corresponding periodic varia-
tions in the elements of terrestrial magnetism produced by these
stresses.
This was the speculation which led the writer to examine such
records of long series of magnetic observations as were accessible
to him, and to carry out the laborious computations of which the
results are given below. It was realized from the first that the
speculation was of little weight. But it was also realized that
the discovery, if real, of the periodicity which it suggested, would
be a distinct advance in our knowledge of the Earth, and might
possibly lead to new lines of attack upon the mysteries of terres-
trial magnetism. Hence the uncertain and seemingly half- stifled
answers which Nature returned to the inquiries of the computer
did not swerve him from his purpose of making a vigorous and an
extensive investigation of the matter.
The following series of observations have been used:
Los Angeles, California; see Reports of the United States Coast and
Geodetic Survey, 1890 and 1891 ; absolute measures of horizontal intensity,
Oct 1882 — Sept 1889; differential measures of horizontal intensities, Dec.
7
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8 /. F. HAYFORD [vol. iv, no. i.]
1882— Feb. 1889 (remainder of series ignored for reasons stated on page 62 of
Report for 1891, Part 2); absolute and differential measures of declination,
Oct 1882— Sept. 1889; absolute measures of dip, Oct 1882— Sept 1889.
Key West, Florida ; see Coast Survey Report for 1874 ; 54 months of
absolute measures of declination between March i860 and April 1866 (not
continuous); differential measures of declination, August i860 — March 1866
(March— July i860 ignored for reasons stated on page 117 of Coast Survey
Report for 1874) ; absolute measures of dip 57 months between Feb. i860 and
Apr. 1866 (not continuous) ; absolute measures of horizontal intensity 55
months between Mar. i860 and Apr. 1866 (not continuous).
EastporT, Maine ; see Coast Survey Report for 1865, absolute measures
of declination, Aug. i860— July 1864 ; absolute measures of dip and horizontal
intensity, Jan. i860— July 1864.
Girard College, Philadelphia, Pennsylvania; differential measures
of declination, June 1840— June 1845, and differential measures of horizontal
force, July 1840 — June 1845.
Bombay, India ; differential measures of declination, July 1867 — Dec. 1890.
Batavia, Java; declination, horizontal intensity, and dip, Jan. 1884 —
Aug. 1895 (portion of series before 1884 omitted on account of discontinuity,
and Sept — Dec. 1885 omitted so as to leave an integral number of 14- mouth
period).
The monthly means of the above series were used in the inves-
tigation after being corrected for secular changes and for variations
with a period of one year. These secular changes and annual varia-
tions were eliminated by using their values as given with the pub-
lished results if so given, and in other cases a special computation
was made to determine them.
The next step was to arrange these monthly values in fourteen
groups corresponding to the fourteen different months in each
latitude-variation period in such a way that all the values in any
one group corresponded to the same phase of the latitude variation.
In doing this, the fact that the latitude-variation period is not ex-
actly fourteen months has to be taken into account. For each sep-
arate series the average length of the latitude-variation period was
first derived, for the interval of time covered by that series, from
Professor S. C. Chandlers published results in Astronomical Journal,
No. 322. It will be observed, from the expressions given on pages
7-8, that this period varied, for the intervals of the various series,
from 425 days to 434 days. The monthly values were then arranged
in fourteen groups as indicated above, — each value being placed
in the group nearest to which it occurred (or in some cases a value
corresponding to the exact time of the group was derived from
adjacent monthly means by a straight-line interpolation). This
approximate treatment of the monthly means will make the derived
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428-DAY PERIOD IN THE EARTH'S MAGNETISM? g
amplitude of the variations, expressed as a sine curve, slightly too
small, and will cause an error in its derived epoch of something
less than 3 for any of the cases in hand.
The results of the grouping are shown in Tables I and II below.
The values given in the two tables are the group means dimin-
ished by a constant which is approximately their mean.
Table I
Station
Los
Angeles
Key West
Key West
Key West
Eastport
Eastport
Element
Abs.
Abs.
Abs.
Abs.
Abs.
Abs.
Dec.
Dec.
Dip.
Hor'l I.i
Dec.
Hor'l I.i
Group I
/
— O.40
/
+O.13
/
+007
4-O.OOI6
/
— 1.18
— 0.002
II
+0.07
+O.47
-O.74
— O.OOI4
4-0.25
—0003
III
— 0.33
— O.17
— O.46
4-O.OO06
4-0.68
—O.003
IV
-H>-75
+O.07
— O.46
4-O.OOI I
-j-O.02
4- O.OO I
v
—0.12
+O.38
+O.44
— O.O024
4-0.28
— O.OOI
VI
+0.28
—O.30
-j-I.26
— 0.0022
-j-0.42
0.000
VII
+0.08
-fo.40
+O.72
— 0.0006
—O.08
4-O.OOI
" VIII
-0.88
+O.16
-043
4-O.OOI I
—O.38
— O.O02
IX
—o.55
—O.08
—O.36
— O.OOI6
+0.45
—0.001
X
+0.23
— O.64
+O.14
4-O.O0O6
-fo.40
0.000
XI
— 0.17
-fo.10
+O.41
-fo.0004
-0.37
4-0.002
XII
+0.23
+0.30
—O.26
—0.0014
—0.55
4-0.003
" XIII
— 0.07
— 0.20
-f-O.30
4-O.0018
—0.17
O.OOO
" XIV
—0.03
— O.IO
—O.58
-j-O.0021
4-0.25
0.000
Date falling in
Group I
Oct. '82.
Apr. '65.
Apr. '65
Apr. 65.
Jan. '60.
Jan. *6o.
1 In British units.
The values of Table I are so small, and there is so little group-
ing of 4- and — signs, that it does not furnish any evidence of a
14-month periodicity. Nor can it be said to furnish much evidence
against the existence of such a periodicity; for these series are
comparatively short, and are subject to comparatively large acci-
dental errors. ,
The series which furnish some apparent evidence in favor of
the existence of the 14-month period are shown in the next Table
(II), arranged in the order of increasing strength of evidence.
Each column of this table seemed to show sufficient indications
of a 14-month periodicity to warrant further investigation. Ac-
cordingly the simple sine curve which most nearly represents the
values of each column was computed by least squares, together
with the probable error of its amplitude. The probable errors were
derived from the residuals furnished by the original monthly values,
and not from those furnished by the means of the fourteen groups,
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* * -- - - ~z z y-i r-
f !"*!::?:£? :f ; /
^•r:r;
::; jr^ rc*r£
* p i _S* ^ Z-^-Z
*,' * Z
£ . =
*» -v>: • -r, ^ ^
• ? t •* — c
* £
j ". S t •» «. _ „},£; - r^« •» ^. _ J p.
1 - ( .
» if
If
; v i c j i c p c5 c c d c' d 1 -
9
1 •
5 -
i o It. *"*
00
i
■fc
ZZ S
s
o 5
i g
§ 3
5 "
1 » *
1 2
1
3
£ : ' : -■•'.= r : , - ;
O
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428-DA Y PERIOD IN THE EARTH'S MAGNETISM? 1 1
as that would result in a probable error, which would evidently be
much too small to represent the truth. The results are given in
Table (III) below, in the order of Table II. As an additional test,
the Batavia and Bombay series were each divided into two series,
and the computation made separately for each half-series, with the
results as given. t= t-t Q is an interval expressed in days. The
divisor of 360 in each case is the period expressed in days.
The division of the series into two parts seems to prove the
very small apparent variation of the declination at Bombay to be
unreal. On the other hand, a similar division at Batavia, as shown
above, apparently indicates that the derived variations of declina-
tion, horizontal intensity, and dip are real at Batavia.
In general, in investigations of terrestrial magnetism, it is found
that the total force at a given point is less subject to variations
than the direction of that force. If that is assumed to be the case
in the present investigation, the maximum of dip should coincide
with the minimum of horizontal intensity, and if the motion of the
pole of the needle is uniform and circular, the maximum of declina-
tion should lie midway between the maxima of dip and horizontal
intensity. It is noticeable that the epoch angles given above, —
the last term in the parenthesis, — indicate that these relations are
nearly satisfied at Batavia. They are, for horizontal intensity 47 °,
and for dip 245 , differing by 198 instead of 180 , and having for
their mean 146 , which exactly coincides with the epoch angle of
the declination. A similar relation is apparent between the declina-
tion and the horizontal intensity at Philadelphia. At Los Angeles,
the only other station at which this test can be applied, it developes
contradictions.
If the computed results shown above be considered in the light
of the computed probable errors, the evidence in favor of the
reality of the 14-month periodicity seems strong. It seems un-
likely that the computed amplitude should be so much larger than
its computed probable error in so many cases among those tried
unless the assumed period is real.
On the other hand, it should be kept in mind that the computa-
tions of the probable errors are based upon the usual assumption
that the various observed values, monthly means in this case, are
independent. An inspection of the residuals shows, however, that
their signs frequently remain unchanged for several months in suc-
cession, apparently indicating some error or disturbing influence
common to such successive months. It is likely, therefore, that
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Tablb III
Station
to
Empirical Formula
Prob. error
of
Amplitude
Remarks
Los Angeles
Oct 15, '82.
c/.ii6ain|jg!r + 7* }
dbc/126
Differential Decl'ns.
Batavia
Jan. 15, '84.
C/.04 am|g!r+i46°}
dbc/.Q4
DifFl Decl'ns; entire series.
i«
0.03 sin{g^r+i8o°}
— —
" first half of series.
••
0.04 sin|^r-(-i35 |
— —
" " second half of series.
Bombay
Jan. 15, '91.
i".9 sinj^r+168 }
y 1429 J
±i"JS
Diff'l Decl'ns ; entire series.
"
«* 8in {S"° T+i670 }
— —
" first half of series.
<l
1.0 sin|5__r-|-349 l
(.429 J
— —
" u second half of series.
Batavia
Jan. 15, '84.
.ooooi8*sin j^-°- r + 47° i
(.4*5 )
•
= haooooi3
DifFl H. Obs'ns ; entire series.
ft
.000028 sin 1^ — r — 23° \
— —
first half.
(t
.000038 sin l^°- t + o2°i
(425 )
— —
second half.
Los Angeles
Oct 15, '82.
.oooo23*sin|^^ r +283 }
U 26 J
•
±0000012
DifTl H. Obs'ns.
Philadelphia
Aug. 15, '41.
0^.65 sin|5^!r-f-i40°|
(420 )
±c/.3i
DifFl Decl'ns.
Batavia
Jan. 15, '84.
0^.44 sini&l t +245°}
(425 )
= bO / .20
Diff'l Dips ; entire series.
«
0.82 sinj^! r +266 )
U25 )
— —
first half.
t«
0.31 sin|^-r-hi73°|
— —
41 " second half.
Key West
Apr. 15, '65.
(/.i 28 sini^r— 67 )
(434 i
±</.o47
Diff'l Decl'ns.
Eastport
Jan. 15, '60.
o / .434 sin] f-—r-f 257 [
1434 )
dK/.^i
Abs. Dips.
Los Angeles
Oct 15, '82.
*&^{j£ T +*&)
d=o / .i03
Abs. Dips.
Philadelphia
Aug. 15, '41.
.oooo73*sin|^- r + 6^1
*
rto.000020
DiflTl H. Obs'ns.
Los Angeles
Oct 15, '82.
!o .oooo86*sinl^- r -j-226 )
1 (426 j
*
drO.000022
Abs. H. Obs'ns.
C. G. 3. units.
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4*8-DAY PERIOD IN THE EARTH'S MAGNETISM? 13
the computed probable errors given above are considerably too
small, and conclusions drawn from them should be received with
great caution.
In the Journal for March, 1898, pages 13-41, is to be found
an able article by Arthur Schuster, F. R. S., "On the Investiga-
tion of Hidden Periodicities," in which the effects upon the
computation of such grouping of the signs of the residuals as
that indicated in the preceding paragraph are carefully considered,
and methods for testing the reality of apparent periodicities are
developed.
It is shown on pages 27-28 of that article that, if the amplitude
of the apparent variations be computed for various assumed periods,
all nearly equal to the period being tested, we may conclude that a
periodicity is real if its computed amplitude exceeds four times the
mean of the other computed amplitudes. It is also suggested that,
to secure approximate independence of the computed amplitudes,
the assumed periods should be such that the successive quotients
obtained by dividing the interval covered by the observations by
the successive assumed periods shall differ at least 0.25. This test
has been applied, with results as indicated below, to the series of
absolute measurements of horizontal force at Los Angeles, that be-
ing the series in which the ratio of the computed amplitude to its
computed probable error is greatest among the results shown above;
also to the series of differential observations for dip at Batavia, that
being the series in which the various kinds of evidence seemed to
point most consistently to a real periodicity.
LOS ANGELES, CALIFORNIA
Absolute Measures op Horizontal Force
Length op Series = 84 Months
Length of
No. of Assumed
Computed
mimed Period
Periods in the Series
Amplitude
dyne
365 days
6.99
O.OOOO36
379 "
6.74
O.OOOOI3
394 "
6.49
O.OOO041
409 "
6.24
O.OOO073
4a6 "
599
0.000086 (14-month period.)
445 "
574
0.000083
465 "
549
0.000086
4S7 "
524
0.000063
513 "
499
O.000103
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14
/. F HAY FORD
BATAVIA, JAVA
Differential Measures op Dip
Length of Series = 140 Months
(VOL. IV, No. I.]
Length of
No. of Assumed
Computed
Assumed Period
Periods in the Series
Amplitude
/
387 days
II.OO
O.42
396 "
IO-75
0.36
406 "
10.50
0.24
416 "
10.25
0.32
426 "
IO.OO
0.44 (14-month period.)
437 "
975
o.53
449 "
9-50
o.54
461 "
925
o.53
473 "
9.00
o.54
Both these tests indicate strongly that there is no sensible
14-month periodicity in these series.
The evidence, taken as a whole, indicates that, if there is a
14-month period in the elements of terrestrial magnetism, much
more accurate series of observations than those now available are
needed to detect it with certainty.
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BEOBACHTUNGEN UBER DIE EIGENELECTRICITAT
DER ATMOSPHARISCHEN NIEDERSCHLAGE.
Von J. Elstbr und H. Geitei*.
Die electrischen Vorgange in dei* Atmosphare lassen sich
zweckmassig unter drei Gruppen verteilen, deren erste diejenigen in
sich schliesst, die auf der Existenz eines periodisch veranderlichen
und im allgemeinen auch von Ort zu Ort verschiedenen electri-
schen Feldes in dem von eigentlichen Niederschlagen freien Luft-
raume beruhen, deren zweite die Storungen umfasst, die sich zu-
gleich mit dem Auftreten von Niederschlagen innerhalb jenes Fel-
des einzustellen pflegen, wahrend die dritte die Polarlichter und
die mit ihnen verbundenen electrischen Wirkungen in sich be-
greift.
Es ist moglich, dass die in diesen Gruppen zusammengefassten
Vorgange, obgleich sie alle das electrische Feld an der Erdober-
flache beeinflussen konnen, im wesentlichen von einander unab-
hangig sind und innerlich nicht enger zusammenhangen als etwa
um ein Beispiel aus dem thermischen Verhalten der Atmosphare zu
wahlen, die durch Insolation des Erdbodens herbeigefiihrte Tem-
peraturerhohung der Luft mit der in absteigenden Stromungen auf-
tretenden Erwarmung, wie sie in dem Fohnphanomen beobachtet
wird.
Obgleich die an zweiter Stelle aufgefuhrten Erscheinungen, die
der Niederschlagselectricitat, wegen ihrer so eindrucksvollen Aeus-
serung im Gewitter die Aufmerksamkeit am meisten auf sich len-
ken mussten und daher auch diejenigen waren, mit denen sich die
Forschung in den beriihmten Versuchen Benjamin Franklins
und seiner unmittelbaren Nachfolger zuerst beschaftigte, so sind sie
doch in der Folgezeit gegeniiber der ersten und dritten Gruppe
weniger beachtet worden. Man irrt wohl nicht, wenn man diese
Vernachlassigung auf die grossen Schwierigkeiten zuriickf lihrt, die
sich gerade hier einer systematischen Untersuchung entgegenstel-
len. In der That ist das electrische Feld der Atmosphare wahrend
des Falles von Niederschlagen in so verwickelter und verwirrender
Weise veranderlich, dass die Aussicht gering erscheint, irgend
welche Regeln seines Verlaufes zu finden.
Auf der andern Seite ware ein Erfolg auf diesem Gebiete doch
15
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16 / ELSTER UND H. GEITEL [vol. iv, no i]
nicht ohne Bedeutung. Man vergegenwartige sich nur, dass die
electrischen Vorgange im Gewitter in ihrem Zusammenhange mit
andern uns bekannten und dem Experimente zuganglichen Er-
scheinungen noch immer nicht einwandsfrei und ausreichend dar-
stellbar sind.
Eine einfache Ueberlegung geniigt, um einen Begriff davon zu
gewinnen, in wie complicierter Weise das electrische Feld in einem
angenommenen Punkte der Atmosphare wahrend des Falles von
Niederschlagen bestimmt ist
Man betrachte es als die Summe dreier Felder, die der Reihe
nach von einer Eigenladung der I<uft, von der der Niederschlage
und endlich von der durch die Influenz der beiden vorigen auf der
Erdoberflache hervorgerufenen electrischen Schicht herriihren.
Bedenkt man nun, dass sowohl die Niederschlagsteilchen wie
auch die Luft selbst in steter Bewegung begriflFen sind, und dass
die ersteren nach gewisser Zeit in Contact mit dem Erdboden gera-
ten und ihr Potential mit dem der Erde ausgleichen, so kann das
Hin- und Herschwanken der Feldintensitat nicht iiberraschen,
selbst wenn man von der Existenz veranderlicher electromotori-
scher Krafte, von Influenzwirkungen auf die Niederschlage selbst
und von Entladungen ganzlich absieht. —
Indessen ist offenbar die Moglichkeit vorhanden, wenigstens die
eine der oben genannten, die Feldintensitat bestimmenden Ursa-
chen aus ihrem Verbande mit den iibrigen loszulosen, indem man
die Niederschlage in einem isolierten Gefasse auffangt und ihren
electrischen Zustand fur sich bestimmt.
Hierdurch erledigt sich zunachst die wichtige Frage, ob iiber-
haupt an den Niederschlagen merkliche Electricitatsmengen haf-
ten, und wenn man zugleich mit diesen Beobachtungen fortlau-
fende Bestimmungen der Intensitat und des Vorzeichens des
Potentialgefalles verbindet, so lasst sich vielleicht ein Urteil dar-
iiber gewinnen, welcher Anteil der Eigenelectricitat der fallenden
Niederschlage an der Resultante der oben genannten drei Einzel-
felder zuzuschreiben ist.
Ueberlegungen dieser Art veranlassten uns schon vor mehreren
Jahren 1 Beobachtungen iiber die electrische Natur der Nieder-
schlage anzustellen ; wir haben diese mit vervollkommneten Hilfs-
1 Vgl. J. Elster und H. Geitel, Ueber eine Methode, die electrische Natur der
atmospharischen Niederschlage zu bestimmen, Meteorolog. Zeitschrift V . > p. 95,
1888; und Beobachtungen, betreffend die electrische Natur der atmospharischen Nie-
derschlage, Sitzungsber. der K. Akademie in Wien. XCIX. Abth. Ila, p. 421, 1890.
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EIGENELECTRICITAT DER NIEDERSCHLAGE 1 7
mitteln bis zum Jahre 1893 fortgesetzt. Einen kurzen Ueberblick
iiber einen Teil der spateren Resultate hat der eine von uns auf der
Versammlung deutscher Naturforscher in Halle im Jahre 1890
gegeben. 1 In der Hoffnung, dass auch von anderer Seite solche
Beobachtungen angestellt werden wiirden, haben wir wegen ge-
wisser noch zu besprechender Mangel unserer Methode von einer
eingehenden Veroffentlichung bis jetzt abgesehen.
Da aber inzwischen von ahnlichen Untersuchungen nichts be-
kannt geworden ist, so erlauben wir uns im Folgenden eine Aus-
wahl unserer Beobachtungsergebnisse mitzuteilen in dem Wunsche,
hierdurch zur Fortsetzung der Arbeit anzuregen. Zuvor aber wird
es erforderlich sein, das von uns angewandte Verfahren auseinan-
derzusetzen.
Wie schon bemerkt, handelt es sich darum, zwei zeitlich voll-
kommen parallele Beobachtungsreihen zu gewinnen. Die eine
soil den Verlauf der Intensitat der electrischen Kraft an einem
festen Punkte iiber der Erde darstellen, der moglichst nahe dem
Behalter liegt, in dem die Niederschlage aufgefangen werden, die
andere soil ein Maass fur die Electricitatsmengen geben, die gleich-
zeitig in der Zeiteinheit durch die Niederschlage dem Erdboden
an dieser Stelle zugefiihrt sind.
Die erste Forderung, die also nichts anderes als die Messung
des Potentialgefalles an ein und demselben Punkt wahrend des
Niederschlagsfalles bedeutet, begegnet den schon erwahnten
durch die Inconstanz des Feldes bedingten Schwierigkeiten.
Es ist eine Messvorrichtung zu construieren, die mit gleicher
Bequemlichkeit und in schneller Folge sowohl sehr hohe Poten-
tialdifferenzen von mehreren Tausend Volt, wie auch kleinere bis
etwa 100 Volt zu bestimmen erlaubt, wahrend zugleich die Capa-
citat des gesamten Apparats so klein sein muss, dass es den schnel-
len Schwankungen des Feldes von positiven zu negativen Extremen
folgen kann.
Dabei darf allein die eigentliche Collectorvorrichtung (die
Flamme oder bei einem "Waterdropper" die Auflosungsstelle des
Strahles) der Wirkung des zu messenden Feldes ausgesetzt sein,
da sonst bei plotzlichen Schwankungen seiner Intensitat (bei einem
Blitze) die auf der exponierten Oberflache frei gewordene Influenz-
ladung in das Electrometer zuriickstromen und einen stossweisen
1 H. Geitel, Beo achtungen, betreffend die electrische Natur der atmosphari-
schen Niederschlage. Verhandlungen der Gesellschaft deutscher Naturforscher
und Aerzte. 64. Versammlung. Teil II, p. 25.
3
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1 8 / ELSTER UND H. GEITEL Lvol. iv, no. i.]
Ausschlag im Sinne einer plotzlichen Umkehrung der Kraftrich-
tung hervorrufen wiirde.
Es leuchtet ein, dass eine rein statische Messungsmethode, die
diesen Anforderungen geniigt, schwerlich ausfiihrbar sein wird.
Wahrend wir uns deshalb bei den erwahnten, schon veroffentlich-
ten Beobachtungen auf blosse Zeichenbestimmungen des Potential-
gefalles beschrankt hatten, haben wir uns seit 1890 durch ein Ver-
fahren zu helfen gesucht, das auf der Abzweigung einer Teilspan-
nung aus einem stromdurchflossenen Leiter beruht.
Figur I
Als Collector dient ein "Waterdropper", dessen Reservoir im
Innern eines Zimmers im ersten Stocke des Hauses auf einem
MascarV schen Isolierstatif M (Fig. I) ruht, wahrend das Ende des
Ausstrohmungsrohrs nur wenige Centimeter iiber die Bnistung des
Fensters in's Freie hinausragt. In das Reservoir wird von oben
eine mit Wasser gefullte geraumige Flasche F umgekehrt hinein-
gestellt und in dieser Lage durch eine Metallbriicke wie in einer
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EIGENELECTRICITAT DER NIEDERSCHLAGE
19
pneumatischen Wanne festgehalten, so dass, sobald das Niveau des
Wassers die Oeffnung der Flasche erreicht hat, die Ausstromung
des Strahles in bekannter Weise mit constanter Geschwindigkeit
erfolgt. Von dera Collector flihrt ein Leitungsdraht zunachst zu
einem Bohnenberger'schen Electroscope N und von dort in die
eine von zwei Metallplatten A und B t zwischen denen ein etwa
30 cm. langer und 4 cm. breiter Papierstreif ausgespannt ist. A
ist isoliert, wahrend von B aus eine Leitung zur Erde fiihrt. Da
der Papierstreif ein, wenn auch unvollkommener Leiter der Elec-
tricitat ist, so wird sich, sobald der "Waterdropper" unter der
Wirkung einer ausseren electrischen Kraft in Thatigkeit ist, ein
Strom herstellen, der vom Collector iiber das Bohnenberger'sche
Electroscop durch den Streifen zur Erde fliesst. Zwischen A und
B bildet sich dabei im allgemeinen ein linearer Abfall der Span-
nung heraus, und diese kann daher an dem mit einem verticalen
Draht CZ?alsGleitcontact ausgestatteten Exner'schen Electroscope
E an beliebigen Stellen des Streifens gemessen werden. Das Elec-
troscop wird von einem leicht verschiebbaren, aber stabilen Halter
getragen, sein Gehause steht durch einen dunnen Draht mit der
Erde in leitender Verbindung. Auf dem Papierstreifen A B sind
von B aus anfangend 5 verticale Bleifederstriche gezeichnet, deren
Abstand von B ^ , ^, J, J, \ der ganzen Lange des Streifens be-
tragt, sie werden im folgenden als Marke 20, 16, 8, 4, 2 bezeichnet
werden ; dem Endpunkte des Streifens in A wiirde demnach die
Marke 1 zukommen.
Angenommen nun, die Feldintensitat sei so gross, dass, wenn
der Gleitcontact C D auf Marke 1 steht, das Electrometer zur Mes-
sung nicht ausreicht, d. h. dass die Blattchen an die Schutzbacken
schlagen, so riickt man in der Richtung nach B bis zu einer Marke
weiter, bei der die Messung moglich geworden ist und multipliciert
die gefundene Voltzahl mit der Ordnungszahl der Marke. Reicht
selbst, was selten vorkommt, Marke 20 nicht aus, so kann man
leicht einen Punkt zwischen ihr und der zur Erde abgeleiteten
Platte B finden, in dem die Messung ausfiihrbar wird und die
zugehorige Marke schatzen.
Zunachst geben die so erhaltenen Zahlen nur ein relatives
Maass des an der Auflosungsstelle des Wasserstrahles herrschen-
den Potentialgefalles und sind daher nur so lange unter sich ver-
gleichbar, als das Leitungsvermogen des Papierstreifs constant ge-
blieben ist. Fur ein und denselben Niederschlagsfall trifft dies
wohl einigermassen zu, da der Streifen wahrend der Dauer der
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20 / ELSTER UND H. GEITEL [Vol. iv. no. u
Beobachtung im Zimmer vor starkem Temperatur- und Feuchtig-
keitswechsel geschiitzt ist. Weiter auseinander liegende Messungs-
reihen sind dagegen direct nicht mit einander vergleichbar.
Da die ganze Vorrichtuug dauernd zur Erde abgeleitet ist, so
kann eine Anhaufung freier Electricitat bei plotzlicher Schwan-
kung des ausseren Potentialgefalles nicht eintreten, der Apparat
verhalt sich in der Beziehung wie ein statisches Electrometer von
sehr kleiner Capacitat, auch die Tragheit des "Waterdroppers", der
ein isoliertes Leitesystem nur langsam auf das Potential der Auf-
losungsstelle des Strahles laden wiirde, spielt hier keine so storende
Rolle, da eine Votentialausg/eichung uberhaupt nicht stattfindet.
Ein Mangel der Methode liegt darin, dass in geheizten Rau-
men die Leitfahigkeit des Papiers zu gering wird ; man erkennt
dies daran, dass das Verschwinden hoher Ladungen eine merk-
bare Zeit erfordert, hiermit verbunden konnen auch Storungen
vorkommen, die auf einer Polarisation des Papierstreifens beruhen.
Es ist uns nicht gelungen ein besser geeignetes halbleitendes Ma-
terial zu finden.
Um eine, wenn auch nur angenaherte Vergleichung der zu ver-
schiedenen Zeiten erhaltenen Reihen und zugleich eine rohe Be-
rechnung der absoluten Feldstarke zu ermoglichen, hat man einen
giinstigen Zeitpunkt wahrzunehmen, in dem das Feld einiger-
massen constant und mittelst eines Flammencollectors direct am
isolierten Electroscope messbar ist. Durch Vergleichung der so
direct und der gleichzeitig an Marke i des Papierstreifens gefun-
denen Voltzahlen erhalt man einen Factor, durch den man die
Messungen auf den Ort des Flammencollectors reducieren kann.
Kennt man fiir diesen schliesslich den Reductions factor auf einen
in ein Meter Hohe iiber einer Ebene gelegenen Punkt, so wiirde
sich auch der absolute Betrag der Feldstarke in Volt/Meter ange-
ben und dadurch eine Vergleichung verschiedener Reihen erzielen
lassen. Indessen ist zu beach ten, dass diese Reduction die angege-
bene Bedeutung in Wirklichkeit nur dann haben konnte, wenn die
Luft keine electrischen Massen enthielte, das Feld iiber ebenem
Erdboden also homogen ware. Der Sinn der reducierten Zahlen
ist daher der, dass sie den Betrag der Feldstarke in absolutem
Maasse iiber ebenem Erdboden angeben wiirden, unter der in
Wahrheit nicht zutreffenden Voraussetzung, dass die Atmosphdre frei
von electrischen Massen ware.
Eine Berechnung des an einem Orte zu erwartenden Potential-
gefalles aus dem gleichzeitig an einem andern beobachteten ist
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EIGENELECTRICITA T DER NIEDERSCHLAGE 2 1
selbstverstandlich hier unausfiihrbar, da uber die Verteilung der
electrischen Massen in der I^uft wahrend des Niederschlagsfalles
nichts bekannt ist.
Die Thatigkeit desjenigen Beobachters, der die Messung des
Potentialgetalles zu besorgen hat, gestaltet sich nun in folgender
Weise. Nachdetn er den beschriebenen Apparat aufgestellt und
den "Waterdropper" in Thatigkeit gesetzt hat, fiillt er in einem
vorbereiteten Schema mit den Ueberschriften : i. Zeit, 2. Zeichen,
3. Marke, 4. Divergenz, 5. Bemerkungen, die Rubriken in Inter-
vallen von je 1 Minute aus. Unter 1. wird die an der Uhr abgelesene
nach Minuten fortlaufende Zeit, unter 2. das am Bohnenberger'schen
Electroscope erkennbare Vorzeichen der Electricitat, unter 3. die
Marke des Papierstreifs, an der gemessen wird, unter 4. die beobach-
tete Divergenz der Electroscopblatter eingetragen. Ist Veranlassung
vorhanden zu Bemerkungen iiber die Natur der Niederschlage, iiber
Luftbewegung, Blitzeetc, so werden diese kurz in der letzten Spalte
hinzugefiigt. Bei Nahegewittern wird es ofters notwendig, den
heftigen Schwankungen und Zeichenwechseln der electrischen
Kraft in Intervallen einer Viertelminute zu folgen. Haufigere
Zeichen wechsel wie diese — bei unausgesetzten Blitzentladungen
— lassen sich allerdings nur als solche, ohne wirkliche Messung
ihrer Amplitude, notieren. Wenn moglich, wird beim Abschluss
der Beobachtungen, wenn der Niederschlagsfall voriiber und die
electrische Kraft einigermassen gleichbleibend geworden ist, eine
directe Messung des Potentialgefalles am isolierten Electroscope
vorgenommen, zur Bestimmung des Reductionsfactors auf gemein-
sames Maass.
Wahrend der eine Beobachter nach dem beschriebenen Verfah-
ren den Verlauf der electrischen Kraft an dem gewahlten Punkte
aufzeichnet, hat der andere die Eigenladung der fallenden Nieder-
schlage zu messen. Die anzuwendende Methode ergiebt sich aus
folgender Betrachtung. Wollte man etwa die zum Auffangen der
Niederschlage bestimmte Schale durch ein MascarV sches Statif iso-
liert in's Freie stellen, wahrend sie durch einen I^eitungsdraht mit
dem Electrometer in Verbindung steht, so wiirde man, auch ohne
dass Niederschlage hineinfallen, die starksten Schwankungen ihres
electrischen Zustandes beobachten, die offenbar durch die Veran-
derlichkeit des ausseren Feldes induciert sind. Es bleibt nichts
iibrig, als das Auffangegefass, wenigstens so lange das Electrometer
abgelesen wird, gegen diese Influenz durch eine es allseitig umge-
bende metallene und zur Erde abgeleitete Hiille zu schiitzen, auch
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22 /• ELSTER UND H. GEITEL. [vol. iv, no. i]
tiber die gesamte zum Electrometer fuhrende Drahtleitung muss
sich dieser Metallmantel erstrecken, soweit sie im Freien verlauft.
Wir haben deshalb der Auffangevorrichtung die folgende Ge-
stalt gegeben. Figur II.
In etwa 6 Meter Entfernung von der Hauswand, (8 Meter von
der Miindung des oben beschriebenen Tropfensammlers) ist ein
Figur II
Cylinder 5 aus Eisenblech von 128 cm. Hohe und 25 cm. Durch-
messer mit seitlicher Thiir T und conischem Aufsatze aufgestellt,
an den sich ein aus zwei zusammenlegbaren Halbcylindern gebil-
detes Rohr L anschliesst. Dieses fuhrt zu einer Oeffnung im Fen-
ster 1 des im Erdgeschosse liegenden Zimmers, in dem das zu die-
1 Die Scheibe des Fensters ist durch eine Blechplatte ersetzt.
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eigenelectricitAt der niederschlAge 23
sen Messungen dienende Quadrantelectrometer aufgestellt ist. In
dem Cylinder stent auf einem MascarV schen Statif C die Auffange-
schale A aus Zinkblech, von 23 cm. Durchmesser, von ihr aus fiihrt
durch das Rohr L ein frei gespannter Draht g g zum Electro-
meter. 1
Ein kreisfbrmiges Stiick Eisenblech / von etwas grosserem
Durchmesser als der Cylinder ist an einem horizontal beweglichen
Arme so befestigt, dass es in seiner Ruhelage etwa 4 cm. iiber dem
oberen Rande des Cylinders einsteht und so das Auffangegefass
gegen das aussere electrische Feld abschliesst. Durch eine Schnur
kann es vom Electrometerzimmer aus seitlich weggezogen werden,
so dass hierdurch den Niederschlagen der Weg zur Schale frei
gegeben wird, beim Nachlassen der Schnur kehrt es durch die
Kraft der an dem fest eingerammten Eisenstabe N M angebrachten
Feder O von selbst in seine normale Lage zuriick.
Der im Innern des Cylinders iiber der Schale angebrachte
conische Ring P soil die Tropfen zuriickhalten, die beim Auftref-
fen auf den oberen Rand des Cylinders zerspritzt sind. In diesen
abspritzenden Tropfchen liegt namlich eine grosse Gefahr fiir die
Zuverlassigkeit der Beobachtungen. Der obere Rand des Schutz-
cylinders ist in dem kraftigen electrischen Felde, wie es wahrend
des Niederschlagsfalles besteht, mit einer electrischen Schicht von
hoher Dichtigkeit bedeckt ; ein jeder auf ihm zerspritzender Tropfen
wird also eine unter Umstanden nicht geringe Electricitatsmenge
nach alien Seiten hin verbreiten. Gelangen solche Teiltropfchen in
das Auffangegefass, so konnen sie das Ergebniss der Beobach-
tungen falschen. Um diese sehr bedenkliche Fehlerquelle einzu-
schranken, haben wir neben dem soeben genannten conischen Ringe
noch eine weitere Schutzvorrichtung angewandt, indem wir den
Cylinder 5 noch einmal mit einem an vier Pfahlen Q befestigten,
viel weiteren und hoheren offenen Mantel R aus Drahtgeflecht um-
gaben, der einzig den Zweck hat, die electrische Dichtigkeit auf
dem Rande des ersteren zu vermindern, wahrend er selbst so weit
entfernt ist, dass bei ruhiger Luft die an ihm verspritzten Tropf-
chen nicht in die Auffangeschale hineinfliegen konnen. Bei star-
kem Winde ist ohnehin die Beobachtungsmethode wertlos, da
einerseits die Niederschlage nur vereinzelt die tief stehende Schale
1 Als Mascart'sches Statif dient eine Flasche aus Zinkblech, mit seitlichem Tubus
zum Einfuhren von Chlorcalcium, die Glasstange B tragi einen durchbohrten Kork E,
der zum Verschlusse der Flasche dient, so lange sie nicht gebraucht wird. ^ist ein
Trichter aus Zinkblech, der die Oeffnung der Flasche gegen Tropfen schutzt, wenn
die Schale A entfernt sein sollte.
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2 4 / ELSTER UND H. GEITEL [vol. iv, no. i.j
treffen, andrerseits auch solche hineingelangen konnen, die schon
mit Teilen der Erdoberflache (dem Hausdache, Baumen) in Beriih-
rung gewesen sind. Durch diesen zweiten Schutzcylinder wird
ferner erreicht, dass die etwa ira Augenblicke des Oeflhens oder
Schliessens von dem beweglichen Deckel in die Schale abfallenden
Tropfen der ausseren Influenz weniger ausgesetzt sind.
Dass diese Schutzvorriehtungen unter alien Umstanden ausrei-
chen werden, lasst sich mit Sicherheit allerdings nicht behaupten.
Zur Controle haben wir — so lange noch kein Regen fiel —
wahrend eines Fernge witters, das ein mittelst des Flammencollec-
tors gemessenes Potentialgefalle von mindestens + 1200 Volt/Me-
ter hervorrief, nach Entfernung des conischen Schutzringes P
Wassertropfen aus feiner Oeffnung in reichlicher Menge auf den
oberen conischen Rand des Cylinders 5 fallen und dadurch zer-
spritzen lassen. In 30 Sekunden erhielten wir indessen keinen
merklichen Ausschlag am Quadrantelectrometer. Absolute Sicher-
heit gewahrt diese Probe nicht, denn es ist zu bedenken, dass
wahrend eines Nahegewitters die Feldintensitat den Betrag von
+ 1200 Volt /Meter ganz betrachtlich iiberschreiten kann. Wir
werden deshalb bei der Discussion der Resultate auf diese Fehler-
quelle zuriickkommen miissen.
Der zweite Beobachter, der den soeben beschriebenen Apparat
bedient, hat seinen Platz am Fernrohre des auf Spiegelablesung
eingerichteten Quadrantelectrometers. Vor Beginn der Beobach-
tungen ist seine Uhr mit der des andern in Uebereinstimmung ge-
bracht. Sobald die Niederschlage fallen, unterbricht er zunachst
die Erdleitung des Electrometers, zieht mittelst der oben erwahn-
ten Schnur den Deckel von dem AufFangegefass zuriick, notiert
die zugehorige Zeit und beobachtet die Bewegung der Electrome-
ternadel. Sobald ein deutlich messbarer Ausschlag sich herausge-
stellt hat, deckt er durch Nachlassen der Schnur das AufFangege-
fass zu, notiert die Zeit und den beobachteten Ausschlag ein-
schliesslich des Vorzeichens und leitet zugleich das Electrometer
zur Erde ab. Sofort beginnt dann dieselbe Thatigkeit von neuem.
Ist die Diimpfung des Instrumentes gut, so kann eine Beobachtung
der andern in Zeitraumen von % bis y 2 Minute folgen, bei sehr
kraftigen electrischen Anzeichen darf man den Apparat nur wenige
Sekunden offnen, damit nicht die Skala aus dem Gesichtsfelde ver-
schwindet. Bei schwachen Regen- und Schneefallen, deren Eigen-
electricitat haufig gering ist, miissen die Zeiten entsprechend gross
(bis 2') gewahlt werden, damit ein sicher bestimmbarer Ausschlag
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EIGENELECTRICITAT DER NIEDERSCHLAGE 25
erzielt wird. Schliesslich sind alle erhaltenen Zahlen auf dieselbe
Zeitdauer, etwa 5', zu reducieren. Am Ende einer Beobachtungs-
reihe wird dann noch die Empfindlichkeit des Electrometers
mittelst eines Clarkelements bestimmt und die Uebereinstimmung
der Uhren der beiden Beobachter nochmals constatiert. Sorgfaltige
Ueberwachung erfordert die Isolation des Systems, sie ist am An-
fang und Schluss jeder Reihe, sowie auch bei langeren Pausen im
Regenfall zu priifen. Isolationsfehler werden im Sommer haufig
durch feine Faden verursacht, die innerhalb des Schutzcylinders
oder des Schutzrohrs von Spinnen gebildet werden, die beim Re-
genwetter dort Zuflucht gesucht haben ; sie sind durch Auskehren
des Apparats mit einer Biirste oder durch Absengen mittelst einer
Spiritusflamme zu beseitigen.
Um die Beobachtungen in ubersichtlicher Weise wiederzugeben,
haben wir graphische Darstellungen gewahlt. (Siehe die Tafeln.)
Die Abscissen entsprechen der Zeit, deren Einheit die Minute ist,
die Ordinaten der zusammenhangend gezeichneten Curve sind dem
gemessenen Potentialgefalle proportional (wenn nichts dabei be-
merkt ist, wiirde 1 mm. der Zeichnung etwa 50 Volt/Meter ent-
sprechen), die der punctierten geben die am Quadrantelectrometer
beobachteten Ausschlage wieder in der Weise, dass sie pro 1 mm.
das dem Electrometer erteilte Potential in Volt berechnet auf 5'
ausdriicken. Es ist dabei zu beachten, dass das letztere nicht allein
von der electrischen Ladung der Niederschlage, sondern zugleich
von ihrer Ergiebigkeit abhangt. Einigen Anhalt hieriiber sowie
fiber andere Nebenumstande gewahren die beigeffigten Bemerkun-
gen. Zu einer Schatzung der durch die Niederschlage zur Erde
gefuhrten Electricitatsmengen wiirde die Kenntniss der Capacitat
der Auffangevorrichtung einschliesslich der Drahtleitung und des
Electrometers erforderlich sein. Durch einen besonderen Versuch
ist diese zu etwa 144 cm. bestimmt worden. Im allgemeinen ist,
wie gesagt, auf jede Minute eine Messung zu rechnen, haufig wur-
den auch mehrere ausgefuhrt, so dass die Zeichnung bei ihrem klei-
nen Maassstabe die Einzelheiten nicht ganz vollstandig wiedergiebt.
Zu diesen schwer wiederzugebenden Feinheiten gehoren besonders
die stossweisen Aenderungen des Potentialgeialles, wie sie bei
Xahegewittern in Folge von Blitzen eintreten, sie sind meist nach
wenig Sekunden wieder ausgeglichen und z. T. wie oben schon an-
gedeutet, auf die im Momente einer Entladung an der Collector-
dffnung frei gewordene Influenzelectricitat zuriickzufiihren. In
No. 1 sind sie (auch der Grosse nach) mit angegeben. Audi bei dem
4
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2 6 /• ELSTER UND H. GEITEL [vol. iv. no. i]
Gewitter, auf das sich Curve 2 bezieht, traten sie so zahlreich auf,
dass sie bei dem Maassstabe der Figur nicht gut mehr darstellbar
waren.
Nimmt man zunachst an, dass die erhaltenen Curven durch
keine Fehler der Beobachtungsmethode gefalscht sind, so ergiebt
sich als erstes Resultat, dass die Niederschlage ganz erhebliche
Electricitatsmengen, positiver und negativer Art, mit sich fiihren
konnen, insofern sie ofters dem aus Auffangeschale, Drahtleitung
und Electrometer bestehenden Systeme ein Potencial von mehreren
Hundert Volt, fur eine Zeitdauer von 5' berechnet, (in einem Falle
iiber — 1000, vgl. Fig. 12) erteilten. Dabei stimmt das Vorzeichen
der Niederschlagselectricitat mit dem des in unmittelbarer Nahe
gemessenen Potentialgefalles in den meisten Fallen nicht iiberein, es
sind vielmehr sehr haufig die beiden Curven auf entgegengesetzten
Seiten der Abscissenaxe gelegen. Wenn die z. T. sehr hohen Werte des
Potentialgefalles von iiber 10,000 Volt/Meter fur auffallend gehalten
werden sollten, so ist zu bemerken, dass man bei Gewittern und
Schneeboen haufig Funkenentladungen beobachtet, wenn der Col-
lator bis zu der Stellung vorgeschoben wird, in der er bei normalem
Wetter das Potentialgefalle unmittelbar in Volt/Meter zu messen
erlaubt.
Der Gegensatz zwischen dem Vorzeichen der Niederschlagselectri-
citat und dem des gleichzeitig beobachteten Potentialgefalles wurde
zu dem Schlusse notigen, dass das durch die erstere an der Erdober-
flache inducierte Feld in den meisten Fallen von einem andern ent-
gegengesetzten uberwogen wird. Man hatte sich zu denken, dass
mit dem Niederschlagsfalle ein electromotorischer Vorgang verbun-
den ist; indem die eine Electricitatsart durch die Niederschlage zur
Erde gefiihrt wird, entsteht in der Luft oder den Wolken ein stets
wachsender Ueberschuss der entgegengesetzten. Ist diese Deutung
richtig, so miisste sich der Zeichengegensatz mit besonderer Regel-
massigkeit am Ende der Niederschlagsfalle zeigen, da dann (sofern
man von Entladungen absieht) die in der Luft verbliebene Elec-
tricitatsmenge ihr Maximum erreicht hat.
Bedenkt man, dass beim Abzuge einer Regenwolke sowohl das
von ihr inducierte Feld wie auch die der Auffangeschale zugefuhrte
Regenmenge abnimmt, so wiirde man als Abschluss in der Regel
zu erwarten haben, dass die punctierte Linie das ungefahre Spiegel-
bild der zusammenhangenden ist und dass sich beide der Abscissen-
axe nahern. Man vergleiche hierzu die Figuren 1, 2, 3, 4, 5, 7, 8,
14, 16.
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EIGENELECTRICITAT DER NIEDERSCHLAGE 27
Zu Beginn und inmitten eines Regen- oder Schneefalles, wenn
zugleich Tropfen oder Flocken in grosser Menge die Luft erfiillen,
die eine hohe Eigenladung haben, kann das von ihnen hervorgeru-
fene Feld iiberwiegen und das Vorzeichen des Potentialgefalles vor-
iibergehend bestimmen. Von solchen Uebereinstimmungen der
Vorzeichen heben wir hervor : Fig. 1 (von 2 h 48' bis 3 h 13'), Fig.
2 (2 h 23'— 27', 3 h 17', 3 h 26O, Fig. 3 (von 2 h o' bis 2 h 30', fer-
ner kurz vor 4 h), Fig. 4 (anfangs und von 9 h 34'— 40'), Fig. 5
(anfangs), Fig. 6 (anfangs), Fig. 7 (von 7 h 55' bis 8 h 15'), Fig. 8
(um 2 h 50'), Fig. 9 (durchgehends), Fig. 11 (an verschiedenen
Stellen), Fig. 12 und 13 (anfangs), Fig. 14 (um 4 h 35' und 4 h $d)
Fig. 15 (anfangs), Fig. 16 (von 3 h 54' — 57'), Nro. 17 (um 2 h 10').
Wie schon ein fliichtiger Ueberblick iiber die Curven lehrt, ist
das Vorzeichen des electrischen Feldes wahrend des Niederschlags-
falles besonders haufig negativ, doch kommen auch anhaltende und
hohe positive Werte vor. Das Vorherrschen der negativen ist ohne
Zweifel der von Herrn Lenard naher erforschten Wasserfallelec-
tricitat zuzuschreiben, d. h. auf die negative Electrisierung der Luft
am Erdboden durch die zerspritzenden Regentropfen zuriickzu-
fiihren. 1
Einige Einzelheiten scheinen uns noch eine besondere Erwah-
nung zu verdienen. Es ist dies zunachst die hohe Eigenelectricitat
des zuweilen mit Hagel vermischten Gewitterplatzregens, vgl. Fig.
2 (3 h 15—30'), Fig. 7 (7 h 43'), Fig. 10 (6 h 7'— 6 h io^, Fig. 14
(4 h 53'— 55'), Fig. 17 (2 h 11'— 14'). In den vier letzten Fallen
beachte man die verhaltnissmassig kleinen Werte des gleichzeiti-
gen Potentialgefalles. Aber auch sparlicher Staubregen aus dem
Rande einer Gewitterwolke kann stark electrisiert sein, wie Fig. 5
und 16 zeigt. Die Figuren 8, 9, 11, 12, 15, 18 stellen Regen- und
Schneefalle nicht gewittrigen Characters dar; man erkennt, dass
auch bei solchen starke Schwankungen des Potentialgefalles und
betrachtliche Ladungen der Niederschlage vorkommen. Von be-
sonderem Interesse ist der Schneefall (Fig. 12) mit den anfangs
iibereinstimmend, zum Schluss entgegengesetzt verlaufenden Cur-
ven. Leider herrschte dabei lebhafter Wind, der die Schneegrau-
peln in schrager Richtung mit sich fiihrte, auch war es nicht mog-
lich den Reductionsfactor fur das electrische Feld zu bestimmen.
1 Eine gute Vorstellung davon, wie das Potent ialgefalle an der Erdoberflache
durch mehrere in der Atmosphare iiber einander gelajjerte electrische Schichten be-
stimrat ist, geben die Rechnungen von Herrn Linss : Meteor. Zeitschrift IV, p, 345 .
1887.
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28 /- ELSTER UNO H. GEITEL [Vol. iv, no. i.]
Ebenfalls etwas durch Wind beeintrachtigt, aber sehr merk-
wiirdig sind die in Fig. 1 1 dargestellten, wahrend eines anhaltenden
Regenfalles gewonnenen Beobachtungsreihen. Offenbar hat man
es hier mit einer Erscheinung zu thun, die mit den von v. Helm-
holtj. nachgewiesenen Wolkenwogen zusammenhangt ; in iiberra-
schender Weise tritt an der Figur die anfangs regelmassige Perio-
dicitat der electrischen Thatigkeit hervor. (Der Maassstab fiir das
Potentialgefalle ist hier das funffache des sonst gewahlten.)
Die Discussion der Beobachtungsresultate ist, wie vorher be-
merkt, unter der Voraussetzung durchgefuhrt, dass sie den wahren
Verlauf der Erscheinungen wiedergeben. Nun konnen wir leider
nicht verhehlen, dass wir in betreff der unbedingten Sicherheit
dieser Annahme noch einige Bedenken hegen.
Die Moglichkeit, dass Niederschlagsteilchen in die Auffange-
schale gelangen, die schon mit der Erdoberflache in leitender Ver-
bindung gewesen sind, erscheint durch die getroffenen Vorkehrun-
gen noch nicht vollig ausgeschlossen, und gerade der Umstand,
dass solche „verirrten" Tropfen eine dem Vorzeichen des electri-
schen Feldes entgegengesetzte Ladung haben, also auch den so
haufig constatierten entgegengesetzten Verlauf der beiden Curven
bewirken wiirden, verstarkt den Verdacht.
Fur die Zuverlassigkeit der Resultate spricht dagegen die doch
oft genug vorhandene Uebereinstimmung der Vorzeichen, die Un-
abhangigkeit der Ladung des Regens von der Hohe des herrschen-
den Potentialgetalles, sowie der schon hervorgehobene Umstand,
dass der Zeichengegensatz am Ende des Regenfalls besonders deut-
lich zu Tage tritt. Auch die schon friiher 1 mitgeteilte Wahrnehmung,
dass beim Falle grossflockigen Schnees jede einzelne in die Auf-
fangeschale sinkende Flocke ein Fortrucken der Skala des Electro-
meters bewirkt, beweist das Vorhandensein einer sehr merklichen
Eigenladung.
Will man trotzdem die ausserste Skepsis festhalten, so bleiben
doch die Falle von Zeichenubereinstimmung als reell bestehen, sie
genugen zu der Erkenntniss, dass sowohl positive wie negative
Ladungen in Verbindung mit den Niederschlagen auftreten konnen.
Die Resultate der friiheren Beobachtungen, bei denen wir neben
der Untersuchung der electrischen Natur der Niederschlage noch
keine Messungen des Potentialgefalles, sondern nur Bestimmungen
seines Vorzeichens ausfuhrten, werden durch die im vorigen mit-
geteilten durchaus bestatigt. Da von einer weiteren Haufung von
1 Wien. Ber. I. c, p. 430.
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EIGENELECTRICITAT DER NIEDERSCHLAGE 29
Daten ein Gewinn zunachst nicht erwartet werden konnte, so haben
wir seit einigen Jahren diese Arbeiten abgebrochen. Sehr wichtig
wiirde eine Controle von anderer Seite sein, und wenn diese, nicht
ohne Bedenken erfolgte Veroffentlichung die Wirkung hat, weitere
Beobachtungen sowie Vervollkommnungen derMethodeanzuregen,
so wiirde sie damit ihren Hauptzweck erfiillt haben.
Wolfenbiittel, im Januar 1899.
Zusatz bei der Corrector. In Riicksicht auf eine vor kurzem erschienene
und in dem vorliegenden Hefte besprochene Arbeit von Herrn W. Trabert
fiigen wir noch eine Schatzung der Electricitatsmenge bei, die fiir den
Fall der starksten von uns beobachteten Electrisierung des Gewitterregens
(am 11. Mai 1892, Pig. 17) in der Secunde dem Quadratcentimeter der Erd-
oberflache zugefuhrt ist. Rechnet man 600 Volt als Maximalwert des in 5'
erreichten Potentials des Leitersystems von 144 cm. Capacitat, so ergiebt
sich, bei Beriicksichtigung des Durchmessers der Auffangeschale (23 cm.)
eine Electricitatsmenge von etwa 76 X io -14 Coulomb pro Secunde und
Quadratcentimeter.
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THE PHYSICAL DECOMPOSITION OF THE EARTHS
PERMANENT MAGNETIC .FIELD— NO. i. THE AS-
SUMED NORMAL MAGNETIZATION AND THE
CHARACTERISTICS OF THE RESULTING RESIDUAL
FIELD. 1
By L,. A. Bauer.
The object of this paper is to resolve the earth's so-called per-
manent field into component ones physically in terpre table. It is
an elaboration of a preliminary communication read in 1896 before
the American Association for the Advancement of Science and the
British Association, and entitled " On the Component Fields of the
Earth's Permanent Magnetism." 2 In this first paper the deduc-
tions were based on the measured magnetic components at 84 sym-
metrically distributed points; namely, at the intersections of merid-
ians 30 apart, with the parallels of latitude ± 6o°, ± 40 , dt 20 ,
and the equator. The present investigation, on the other hand,
depends upon the measured magnetic components at 1800 points,
situated at the intersections of meridians, 5 apart, with the 5 par-
allels between 6o° N. and 6o° S.
If we take a cursory glance at a series of magnetic charts of the
earth, we are at once impressed with the complexity of the dis-
tribution of its magnetism. Turn to an isogonic chart, for instance,
and behold the peculiar condition of things existing at the present
time in Eastern China and Japan. You will note that here we have
a closed curve along which the needle is " true to the pole." Within
the oval the needle everywhere points W. of N., while outside,
the compass everywhere bears East. What is the cause of the pe-
culiar distribution in this region? Is it due, for example, to pecul-
iarities in the geological structure of this part of the earth? We find,
moreover, that this oval is not a permanent feature of that region.
It has formed only within the present century, and is now en-
larging. In the sixteenth century we had a somewhat similar state
of affairs in the Atlantic Ocean, only that in this case the oval in-
closed places where the needle stood East, instead of West as in
the Asiatic oval.
1 Presented for the author before the Philosophical Society of Washington on
Tanuary 21, 1899, by John Fillmore Hayford, of the United States Coast and Geodetic
Survey.
* Printed, in abstract, in Terrestrial Magnetism, Vol. I, p. 169.
5 33
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34
L. A. BAUER l Vol. IV, No. i.]
Again, observe the tremendous curvature of the lines of equa
dip and of equal horizontal intensity in passing from the Cape of
Good Hope to Cape Horn.
Many attempts have been made to refer the complexity of , the
magnetic distribution entirely to purely geological causes — e. g., the
distribution of land and water— but the deductions thus far made
have not been generally accepted, the method of inquiry usually
being of a more or less superficial nature.
From a mathematical standpoint the analysis of the earth's mag-
netism has reached an order of perfection chiefly through the
labors of Gauss and Schmidt, which leaves comparatively little to
be desired in this direction. The latest attempt at a complete
mathematical analysis — that by Schmidt — has resulted in the fol-
lowing conclusions:
The earth's magnetic force consists of three parts, viz. : i. The
greatest part — this is to be referred to causes within the earth's
crust, and possesses a potential. 2. The smallest part, about -h of
the entire force— this is due to causes outside the earth's crust, and
likewise possesses a potential. 3. A somewhat larger part than the
preceding — this does not possess a potential, and, in consequence,
points to the existence of vertical earth-air electric currents. These
currents amount, on the average, for the entire earth's surface, to
one-sixth of an ampere per sq. km.
Gauss expressed the earth's magnetic potential in solid spher-
ical harmonics to terms of the fourth order, which included 24 co-
efficients. He supposed, however, that the entire magnetism was due
to causes within the earth's crust. Schmidt, on the other hand, does
not assume ad initio the existence of a function, the potential, to
which all the components of the force (northerly, easterly, nadir)
can be referred, and, consequently, has made a separate adjustment
of each of the three components, obtaining three spherical har-
monic expressions instead of one. He has carried his expressions
to terms of the 6th order.
While, then, we have succeeded fairly well in resolving mathe-
matically the earth's total field into component ones, we have made
as yet very little progress in its physical analysis.
The spherical harmonic of the first order, entering into Gauss's
and Schmidt's expressions, can be referred to a uniform magnetiza-
tion of the earth, about a diameter inclined to the axis of rotation,
or to causes similar in effect to such a simple magnetization. The
higher harmonic terms have not yet been interpreted. When we
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DECOMPOSITION OF EARTH'S MAGNETIC FIELD
35
speak of the earth's magnetic moment, or of the magnetic axis,
we have in mind only the uniform magnetization. Suppose we
were to deduct from the total field the uniform magnetization, what
characteristics would the residual field possess?
Is this residual field a heteorogeneous or an anomalous one?
That is, does it exhibit features which can be brought directly in
harmony with geological features? Manifestly this should be to a
greater or less extent the case, if the distortion of the isomagnetic
lines is to be referred principally to such causes.
My paper in 1896 was an attempt to answer these questions, the
method employed being a graphical one, as the eye is often quick
to detect what the mind is slow in comprehending.
The present paper, as stated, is a re-investigation of the charac-
teristics of the residual field, this time as based upon the most com-
plete data at present available. A word with regard to this mate-
rial. It consists of the three rectangular components, X m , positive
north, Y m% positive East, and Z m , positive vertically downwards, at
1,800 points on the earth's surface, situated 5 apart in latitude and
longitude, between parallels 6° N. and 6° S. There are thus 72
points on each of 25 parallels, embracing in all 5,400 magnetic
components. These components have been computed to five deci-
mals C. G. S. units, by H. Petersen, of Kiel, with the aid of
the values of the declination, inclination, and horizontal intensity
at the 1,800 points as furnished him by Professor Neumayer, direc-
tor of the German Seewarte, who scaled them from his excellent
series of magnetic maps for 1885. These maps were based upon
the most complete data available at the time, many thousand obser-
vations being utilized. The components X m% Y m , Z m , are, there-
fore, not derived from directly observed quantities, but are based
upon them. I shall refer to them, hereafter, as the "measured"
components. Valid objections might be made to the effect that
this material, from one cause or another, is more or less defective in
certain regions, and that abnormal values — locally or regionally dis-
turbed values — have been eliminated to a greater or less extent.
It should be remembered, however, that we are simply endeavoring
to localize those centers of disturbance affecting the entire earth,
and that, hence, for such a broad investigation the utilized material
will undoubtedly prove more than ample. Indeed, the sequel will
show that the few points (84) used in the first paper are sufficient
to indicate the chief peculiarity of the residual field.
Dr. Schmidt, courteously supplied me, late in 1896, with the 5,400
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36 L. A. BAUER [Vol IV, No. i.]
measured components, 1 computed by Petersen, and I have already
utilized the 1,800 Y values in an investigation on "Vertical Earth-
Air Electric Currents," which I had the honor to present before
this Society two years ago. Multifarious duties prevented me from
resuming my private investigations until a few weeks ago, when I
availed myself of a generous offer made by three of my students,
to assist me in the laborious computations involved in this investi-
gation. I desire to express here, my grateful appreciation of the
faithful and enthusiastic service rendered me by these three gentle-
men: Henry William Vehrenkamp, John Adams Fleming, and
Harry Dickman. They gave up their Christmas holidays in the
prosecution of this work, taking part in all the computations and
in the drawing of the diagrams accompanying the paper.
The first question to be settled in this inquiry is, What shall be
taken as the normal distribution of the earths magnetism? The
simplest supposition would be that the earth is uniformly magnet-
ized about the rotation axis. This was my starting-point in a paper
presented before this Society in May, 1895. The resulting residual
field clearly revealed the fact that a portion could be referred to a
magnetization about a diameter lying in the plane of the equator,
and the chief deduction was, that "the principal phenomena of the
distribution of terrestrial magnetism can be regarded as produced
by two rectangular magnetic systems, a polar and an equatorial,
the former of about five or six times the strength of the latter."
In the next attempt, I combined the two uniform rectangular sys-
tems into one, and thus obtained, as the normal distribution, that
resulting from a uniform magnetization about a diameter inclined
ii°. 7 to the rotation axis. This was done in the paper before the
American Association already alluded to.
In the present paper, I again define, as the normal magnetic
distribution, that which can be ascribed to a uniform magnetization
(or to equivalent effects) about an inclined diameter. This is the
most general, simple supposition that can be made ; for the uniform
magnetizations about various diameters, no matter how many we
may have, can all be separately resolved into two magnetizations,
one about the rotation axis, and the other about a diameter in the
1 These have since then been published; see "Der magnetische Zustand der
Erde zur Epoche 1885, analytisch dargestellt von Adolf Schmidt," Aus dem Archiv
d. Deulschen Seewarte, Hamburg, 1898, [The following typographical errors occur
in the printed table : Z for «=3o°, 7=25°. should be 46807 instead of 46809, and for
w=8o°, /=2i5°, 13852 instead of 11852; X for w=45°, ^150°, should be 25864 instead
of 26864.— Ba.]
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DECOMPOSITION OF EARTH'S MAGNETIC FIELD 37
equatorial plane. The component magnetizations can then be re-
combined into a resultant magnetization about the rotation axis,
and into a resultant magnetization about an equatorial axis. Fi-
nally, the two resultant fields (polar and equatorial) can be com-
bined into a resultant one, symmetrical about an inclined diameter.
As already stated, the first order terms of the Gaussian analysis
express the uniform field about an inclined diameter. We can,
therefore, derive from them the necessary constants for computing
the normal magnetic elements. Thus far the coefficients entering
into the various harmonic terms of the Gaussian analysis have not
been computed independently of each other; their magnitudes,
therefore, are dependent upon the number of terms to which the
expansion is carried. Recently, Schuster has proposed a method
of computing the coefficients of the first and second harmonics in
such a way that their values do not depend upon the number of
terms taken into account. 1 As the proposed method, however, has
not yet been carried out, we adopt the latest and best values of the
earth's magnetic moment and position of magnetic axis, as ob-
tained by Schmidt. 2 Hence, the normal distribution is defined as
that which can be regarded as resulting from a uniform or homo-
geneous magnetization, the axis of which intersects the Northern
Hemisphere in latitude 78 3^.3, and in longitude 68° 30'. 6 W. of Gr.
and the magnetic moment of which has the value .32298 R* t C. G. S.
units, R beintr the earth's mean radius.
The next step is to compute the normal magnetic components
X n , Y n% and Z n> at the 1,800 points for which we have the measured
values, and then to subtract the former from the latter, obtaining
the residual values, X r , Y r , Z r% with the aid of which the residual
magnetic field can then be mapped out.
We next derive the required formulae. The following notation
is used : X t positive north ; Y> positive east ; Z, positive vertically
downwards; H t horizontal magnetic force; F, total force; D y the
declination ; /, the inclination ; <£, the latitude ; u, the co-latitude ;
and A, the longitude counted eastward from Greenwich.
Case I. The earth uniformly magnetized about the rotation axis.
If the H axis of a system of rectangular co-ordinates be taken
coincident with the rotation, or magnetic, axis, and the origin at
»See this Journal, Vol. Ill, p. 124.
* A. Schmidt : Mitteilungen iibcr eine neuc Berechnung des erdmagnetischen
Potentials, 1895, p. 51.
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38 L. A. BAUER [Vol. iv, No. i.j
the earth's center, then the magnetic potential, V, at any external
point P is x
3 **'
where R is earth's mean radius, r, the distance of P from the origin
and fi, the intensity of magnetization per unit of volume.
If P be on the surface then r = P t and
3 3
V
or ^=- = V = — c . cos u , (i)
u being the co-latitude of P and c = — -*•/*, following Schmidt's
notation.
Furthermore
„ dv i dy
(2)
K _ 8,/ _ i 8 ^_
(3)
8y .# sin « ' 8\ '
„ dV ZV d t _, rcos«\
n-COSK
= 2C& ^ ;
Putting r = R,
Z — 2 c . cos « = — 2 V ,
.(4)
H= i/X* + y» = X = c. sin « ,
/" = i/A' 4 + V + Z* = c T /i + 3 cos *u ,
(5)
D = tan- 1 y=o ,
(6)
and
Z
I = tan~ l t>= tan - " 1 (2 cot «) = tan - " 1 (2 tan <£) . (7)
n
CASE II. 7*Atf *arM uniformly magnetized about a diameter not
concident with the rotation axis.
The only change required in the formula for the potential will
be to substitute for u, u\ u' representing the co-latitude reckoned
See, e. g., Encyclopaedia Britannica, Art. Magnetism, equation xxx.
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DECOMPOSITION OF EARTH'S MAGNETIC FIELD
39
from the point of intersection in the Northern Hemisphere of the
magnetic axis with the earth's surface, as the pole of new geo-
graphical co-ordinates, thus
V H '= — c.cosu' . (8)
To find v! in terms of u and A .
In the diagram, P is any point on
the earth's surface, and N H the inter-
section of the magnetic axis with the
surface or the "north magnetic pole"
for the case assumed, u and u n are,
respectively, the co-latitude of P and
N n reckoned from the true pole, iVand
u' the co-latitude of P counted from
N n . In the spherical triangle N n N P t
the angle at N is the difference of
longitude of N n and P> reckoned from
Greenwich positive to the eastward.
Under the assumed magnetization the angle N H PN yjill be the
magnetic declination.
We have then :
cos u' = cos u n cos u + sin u n sin u cos A A
In which
(9)
AA = A« — A.
Substituting (9) in (8) :
V„ = — c cos u n . cos u — c sin u n . sin u cos AX. (10)
Special Cases.
(a) If u H = o , 1. e. magnetic axis coincides with rotation axis
then (10) reduces to:
Vp = — £.cos#. (11)
as already found.
(6) u H = 90 , i. e. magnetic axis lies in equatorial plane, then
(10) becomes
VJ = — c . sin u cos A X . (12)
Comparing the last two equations with (10), we see that V a f is
composed of two potentials, one due to a uniform magnetization
about the rotation or polar axis and the other to a uniform magnet-
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40
L. A. BAUER
[Vol. IV, No. i.]
ization about an equatorial axis. We can resolve thus any uniform
magnetization about a diameter not coincident with the earth's
axis.
We have then in general :
In which
Vp = C . COS U n . COS U = Cp. cos u
VJ = c sin u n . sin u cos A X = c e . sin u cos AX ,
Similarly,
X M = Xp + A^ ,
Xp = Cp . sin w ,
X e = ^ c e . cos k cos A X .
i
y n =y A +y e ,
y, = o,
or
€ ~^dy Rsmu'bX
Y e = c e . sin A X
i d
^r (,#*> sin w cos AX) ,
Z n :=: - Zp + Ze ,
Zp= 2Cp. COS U = — 2 Vp ,
Z e =2c e . sin « cos A X = — 2^' .
H n = y\Xp + Xe?+ Ye % =C.S\nu' .
or
F„ = v >Hf + Z* 2 =r v /i + 3cos V .
tan D = Yn _ c e sin A X
A* £> sin u — c e cos u cos A X '
fsinK N sinAX
c cos «„ sin u — c sin u H cos « cos A X
sin AX
cos u„ sin u — cos u cos AX
Also from the figure, p. 13 :
sin D : sin AX : : sin u n : sin u'
sin AX sin u n
sin D =
1
(13)
(14)
(15)
(16)
(17)
(18)
(19)
sin u
(19a)
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DECOMPOSITION OF EARTH'S MAGNETIC FIELD
Also
cos u n = cos u' cos u + sin u' sin u cos Z?
4i
or
cosZ? =
cos«„ — cos« cosw
sin u sin u
Finally
tan 7 = 2 cot «' = 2 tan <£ ' .
(19*)
(20)
For the adopted normal magnetization, c is = 0.32298 and u n =
1 1° 25./, hence *> = c . cos « = 0.31657 and ^ = r . sin u = 0.06400.
Or, the magnetic moment of the polar uniform magnetization is to that
of the equatorial uniform magnetization as 31657 : 6400, or nearly
as j : i 1 .
With the aid of formulae (14), (15) and (16), the 5400 normal
magnetic components X H , Y n , Z„ were computed to five decimals
C. C 5. They will have a permanent value and will, doubtless, be
required in our future investigations. With their aid recompu-
tations of the coefficients of the various harmonic terms in the
mathematical analysis can be facilitated as they will permit us to
operate with smaller quantities. Any future change in the assumed
values of the earth's magnetic moment and position of magnetic
axis for 1885 will appear as small corrections to the already com-
puted quantities. It will also appear later that the secular changes
in the normal components can be easily taken into account.
The residual components X r = X m — X n , Y r = Y m — Y n and
Z r =zZ m — Z n , for the 1800 points were then derived. Tables I, II,
III, will give some idea of the character and magnitude of the
quantities involved.
Table L-
■ Computed magnetic components for polar magnetization in unit
0.000 / C. G. S.
Lati-
tude
Xp
Yp
Zp
60N
+ 1583
0000
+5483
40
+2425
"
4-4070
20
4-2975
<<
+2165
Equator
+3166
(t
drOOOO
20
+2975
<t
—2165
40
+2425
"
—4070
60S
+ 1583
0000
-5483
1 Cf. the deduction made in the 1895 paper, cited on p 36.
6
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42
L. A. BAUER
[Vol. IV, No. i.)
Tabi,b II. — The computed or normal magnetic components in units 0/0.000/ C. G. S.
[Plus is understood when no sign is given.]
Long.
E. of'
6o°N
O —596
IO —627
20 — 640
30 '-633
40 — 607
50 1—562
60 —501
70 —424
80 —334
90 —234
IOO —1281
Xn ■ Zn
4Q°N
4429
4265
4095
no
120
130
140
— 17
+ 95
+203
4-3°°
150 j+398
160 l-t-479
170 +546
180 -f-596
190 +627
200 4-640
210 +633
220 4 607
23° 1+562,
240 1 4- 50 1
250 +424
260 +334
+234
+ 128
270
280
290
300
3IO
320
330
340
350
1380 5718 2274
14725601:2343
1568 5500 2414 _
1665538824863925
17595280:25563758
18475178126213602;
1928 5085J2681 3459
I998500427333335
2056I4938 2776^234
2IOO 4888)2808 3158
2 1 26 .4856 j 2828 3109
2i37'4844l2836 309o
21314850 2832 3100
21084876 2815 3140
20704921 27863208
20174982^7473303
I950;5059 i2 698i3420
1872 5149 2640 3558
1786 5249 2576 3711
1693 5356 2507 3874
I597 5467 2436 4044,
I50ii5578 2364 4215!
14075686122944381
131815789 2229 4538
1238 5882 '2169 4680
1168 5963 21 17 4804
1 1 10 6029 2074I4906 1
1067 6079 2032 4982
20 N I Equator 20 S
4o°S
6o°S
Xn I Zn Xn
Zn
2895)26063166
293J2405 "
29692197 *'
3007,1987 "
30441784 "
I59I| " j
I4l6| " '
I264 "
II40| " ,
IO46! " 1
9871 " -
963 " I
976 M :
4- 17
— 95
—203
—306
-398
—479
—546
1040
1029
1035
1057
1096
1 149
61 10
6123
6116
6090
6046
5984
121615907
1293I5818
20225031
2014 5050 1
20185040
2035 5ooo :
20644931;
21034837
21524719
22104582,
3079
3111
3139
3161
3178
3189
3194
3i9i
3182 1025
3167 1 108
3146 1224
3120 1 369
3089 1537
3055 1725
3018 1926
29802134:
2942 2343I
2905 2547
2870 2739,
2838 2914'
2811,3066
2788 3191
27713284
2760 3344
27563368
2758 3355
2767 33o6
2782 3222
2804 3106
2830 2962;
286027943166
4- 4693055
+ 2553018
4- 332980
— 1892942
— 4062905;
I — 61 1 12870,
— 797i2838|
— 959 281 1 :
, — 109112788
1 — 1191 2771
,—125412760
I — 12802756
:— 1 266| 2758
j— 121412767
J— 11252782-
j — 1001 2804-
— 8482830, 1
— 668 2860 •
— 46912895,
— 2552931 ;
— 332969
4- 1893007-
4- 4063044-
4- 61113079-
+ 7973m-
-f 959.3139-
4-1091I3161 -
+ 119113178-
4-1254 3189
4-1280 3194-
4-1266 3191 -
4-121413182 -
4-11253167-
4-10013146-
4- 8483120-
4- 6683089-
-17252576
-1926:2507
-2134,2436
-23432364
-25472294
-27392229
-2914 2169
-3066 21 17!
-3191 2074
-3284 2032
-3344 2022|
-3368 20141
"3355 20I8,
-3306 2035
-3222 2064
-3io6'2io3
-2962 2152
-27942210
-26062274!
-24052343!
-2197 2414.
-19872486 1
-17842556
-1591,2621
-14162681
-126412733
-1 140 2776
-10462808;
- 987 2828
- 963 2836
- 976 2832
-10252815
-1 108 2786
-12242747
-1369 2698
-1537 2640I
Xn , Zn
I
-37 1 1 1786—5249
-3874 1693 -5356
-4044 15971—5467
-42151501— 557S
-4381 1407!— 5686
-4538 1318— 57g9
-46801238—5882
-4804 1168,-5963
-4906 1 1 10 — 6029
-4982 1067 — 6079
-503 1 1 1040— 61 10
-5050 1029 —61 23
-50401035 -61 16
-500010571-6090
-4931 1096 — 6046
-48371149J— 5984
-471912161—5907
-4582 1293— 5818
-4429,1380—5718
-4265 1472 —5601
-4095 1568 —5500
-39251665—5388
-37581760—5280
-3602:1847— 5 J 78
-3459'i928— 5085
-3335|i998— 5°°4
-3234I2056 —4938
-3158 2100 -4888
-3109 2 1 26 — 4856
-30902137—4844
-3100 2131 —4850
-31402108I — 4876
-3208I2070 — 4921
-3303 2017 -4982
-342o| 1950 —5059
-355S 1872 —5149
1 Same for all parallels of latitude.
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w
r 1
«
a
<*
!
©
jo
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44
L. A. BAUER [Vol. iv.no. i.j
Description of the "Chart of the Earth's Magnetic Field
after deducting the uniform magnetization."
On the plate opposite is a map showing the distribution of that
part of the earth's magnetism which can not be referred to a uni-
form magnetization about a diameter. The curved lines are the
lines of equal residual vertical force, and the arrows indicate the
direction assumed by a compass setting itself tangent to the lines
of force of the residual magnetism. Let us suppose that we have
eliminated from the earth the uniform magnetic field, then in the
region of the red curves the north end of the needle would point
toward the focus of the red curves.
Thus, in China, where we had the peculiar distribution of
declination, pointed out in the beginning of the paper, the north
end of the needle (red arrow) points toward N v where the residual
vertical force reaches the maximum value in this particular region
of 0.1390 C. G. S. units. Over this point a dip needle would stand
vertical with the north end downward ; in other words, N x is a north
end attracting pole for the residual magnetism.
A still stronger north end attracting pole is found near South
Georgia Island ; viz., N r It will be recalled that here we had the
greatest curvature in the isoclinics and in the isodynamics. At
N t the residual vertical force reaches a maximum value of 0.1639
C. G. S. units.
If we now pass into the regions of the black curves, the south
end of the needle (black arrow) points toward the foci, S x \ S x \ and
S v and over these points the south end of the dip needle points
vertically downward.
The residual field also reveals a weak north end attracting pole
in the United States and a very weak south end attracting pole
near Alaska.
Along the lines marked zero, the residual vertical component is
zero; or, in other words, the actually observed value corresponds
precisely with the value computed under the assumption that the
earth is uniformly magnetized. Along these lines the dip needle,
setting itself simply in obedience to the residual magnetism, would
be horizontal.
A suggestion might be made to the effect that, instead of chart-
ing the lines of equal residual vertical force, it might have been
advantageous to construct the lines of equi-residual potential. I
purposely avoided this, however, for various reasons; e, g., I did
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IPlati; II.]
(Vol. IV, No. i.J
[The curved
regions of the
in units of the
Lai component of the residual magnetic force. Over the
The vertical intensities (large figures) are given
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DECOMPOSITION OF EARTH'S MAGNETIC FIELD
45
not wish to make the assumption that all of the earth's magnetism
can be referred to a potential. If we have electric currents, namely,
which pass from the air into the earth, or vice versa % their effects
would not have been represented on the chart of equi-residual
potential lines, as the magnetic forces resulting from such currents
do not have a potential. It was thus best to deal with the directly
observed quantities — the vertical forces — so as to get the magnetic
effect in its entirety. Moreover, since recent investigations have
shown that, if a portion of the earth's magnetism has no potential,
it will be only a small fraction of the total magnetization, it can be
easily proven that the lines of equi-residual vertical force will corre-
spond very closely with the equi-residual potentials. 1
Below is a table giving the positions of the magnetic poles of
the residual field, and the amounts of the residual vertical force at
these points :
Table IV
Magnetic Poles or Centers of Residual Field in 1SS5.
General Location
Des-
igna-
tion
Lat.
Long.
E. op
Gr.
Res. Vert.
Force
Zr.
Remarks
China, near Peking
N,
35°N.
no
-f'1390
Africa, Soudan
S,"
Mean
Nl
20^
—•1235)
— *io6i J
Shetland Island
60 Nj
0}
30
10
— -1148
South Georgia Island..
N,
50 S
325
-F1639
Strongest pole.
Near Tasmania.
s,
45 S
135
-•1338
United Stales.
N,
42
45
268
+•0844
— '0208
Approximate position. 2
Aleutian Islands
s,
125
The residual magnetization can be broadly characterized as con-
sisting of two main transverse magnetizations, one system lying in
the Northern Hemisphere, the north end attracting pole (Wi) being
east of the south end attracting poles (5*/, 5/0 » an d the other in the
1 In preparing the 1896 paper I drew the equi-residual potential lines, but did not
publish them.
* Precise point must be determined with the aid of the C. and G. S. isomag-
nctic maps.
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46 L. A. BAUER ivol. iv, No. i]
Southern Hemisphere, the direction of magnetization being the
reverse of the former, the north pole (JV 7 ) lying now west of the
south pole (S t ). Note also that the poles of the two systems lie
near the parallels 40 N. and S. and that the opposite poles of the
two systems are roughly north and south of each other.
Now, the remarkable thing is, that this system of magnetization
is analogous to that which causes the diurnal variation of the
earth's magnetism. On the next chart are reproduced the equi-
potential lines of the diurnal variation field for the summer months
of 1870, Greenwich mean noon. These lines, as stated, correspond
closely with the equi-vertical force lines. They have been deter-
mined by Schuster, 1 and while the data used by him were not suffi-
cient to enable him to determine them with all desirable accuracy,
they represent a fair approximation to the truth. In order to repro-
duce the diurnal variation, it is necessary to assume that the whole
system slides around the earth in an east-west direction ; or, what
amounts to the same thing, that it stands still while the earth
rotates under it.
It will be noticed that the foci of these lines are approximately
in latitude 40 N. and S., just as those of the residual field were,
and that, furthermore, they are apart from each other by the same
amount, approximately, in longitude (or time) as were the poles of
the residual field.
Is the similarity in the relative positions of the foci of the
residual field and the diurnal variation field a mere coincidence?
Again, is the fact that the poles of the two fields are approximately
on the parallels of latitude 40 , which play such an important part
in meteorology, a mere coincidence?
In order to perceive the similarities between certain character-
istics of the residual field and those of the diurnal variation, turn
to the next plate giving the vector diagrams in the horizontal plane
for various parallels. Those for the residual field have been drawn
with the aid of the values X r and Y r contained in Table III, and
those for the diurnal field are taken from von Bezold's paper. It
will be noticed that both sets of curves exhibit similar character-
istics with reference to the directions in which the curves are de-
x Phil. Trans. R. S., 1889, Vol. A. The chart herewith reproduced is taken from
von Bezold's paper, " Zur Theorie des Erdmagnetismus." Sitzber. Akad. d. Wiss.
zu Berlin^ 1897, XVIII. Von Bezold drew the chart with the aid of Schuster's com-
putation. The same chart was drawn by me in 1896, and with its aid the deductions
of the 1896 paper were derived.
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Residual Magnetization
X
VECTOR DIAGRAMS
Diurnal Variation (Von Bezold)
Equator.
[For summer in the Northern Hemisphere, 1870.]
47
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48 L. A. BAUER [vol. iv.no. i]
'T.
X
H
s o
* S
» a
*§
?<
«0
^£
< <
ft z
o s
H X
< y
25
> w
B*
o;
«°
£*
si
^x
•J*
H W
55 X
lr *
2 °
2: 2
X
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DECOMPOSITION OF EARTH'S MAGNETIC FIELD
49
scribed, and that the 40 parallels play an important part in both
sets of curves. 1
But while there are certain very pronounced similarities between
the residual field and the diurnal variation field, there is also a
decided difference between the two. In the one, the principal zero
line goes from northwest to southeast; while in the other, from
northeast to southwest. This is due to the fact that the magnet-
izations exhibited by the two charts are just reversed. For the
residual field, the principal north end attracting pole in the Northern
Hemisphere is east of the south end attracting one ; while for the
diurnal variation, the north pole is west of the south one. In short,
for a north pole in the one chart, we ha\re a corresponding south
pole in the other. For the residual field, the north end of the
compass needle points to a focus where the north end of the dip
needle points downward ; while for the diurnal variation field, the
north end of the compass points to a focus where the south end of
the dip needle is attracted downward. This distinguishing char-
acteristic of the two charts, as we shall see, implies that, in the case
of the first, the cause is an internal one, and that, in the case of the
second, the cause is an external one, as already shown by Schuster
and von Bezold.
Is the cause of the earth's residual field — the heterogeneous mag-
netization — to be referred principally to causes within or without the
earth's crust f This question may already be regarded as answered
by the researches of Gauss and of Schmidt, as cited in the intro-
duction. But it may, nevertheless, be interesting to make an inde-
pendent examination with the aid of a method more easily grasped
by physicists in general. This method, suggested recently by
von Bezold, consists in a simple application of the known laws of
electro-magnetism. Consider, for example, the region of the red
lines in China. It can be easily shown that whatever the source of
magnetization may be, that has caused the magnetic distribution in
this region, whether inside or outside the earth, we can obtain pre-
cisely similar effects by a suitable system of electric currents. This
being so, then the question is, Are the electric currents inside the
earth's crust or outside f The compass and the dip needle placed
in the residual field at any point in this region will answer the
1 The vector diagrams in the ZY plane have also been constructed : the direction
of the curves is the same for both hemispheres.
7
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50 £• A. BAUER [Vol. iv, No i.]
question for us. If we apply Ampere's rule l to the observed direc-
tion of the compass (as indicated by the red arrows), it follows that,
if the currents are inside the earth, they must go clockwise around
N v and if they are outside, they must proceed anti-clockwise.
Now, the dip needle, by reason of the fact that the north end points
down, declares that the currents must go clockwise; hence, taking
the combined testimony of the two instruments, the electric cur-
rents must be inside the crust.
In a precisely analogous manner we can show that the currents
for the other poles must be inside the earth. Hence the cause of the
greater portion of the residual field must reside within the earth's
crust. Around the north end attracting poles of the residual field
the currents would proceed clockwise, and around the south end
attracting poles the currents would go anti-clockwise.
Now let us examine the diurnal variation field. Where are the
currents which could produce magnetic effects such as that shown,
for example, by N x , — the focus in 40 north latitude and in 20 west
longitude? Here we have the north end of the needle pointing to
a focus of minimum, instead of maximum, vertical force, as in the
case before mentioned. The dip needle here would declare that the
currents must go anti-clockwise around A^ ; but the compass says
clockwise, if the currents are inside, and anti-clockwise, if the cur-
rents are outside the earth's crust. Hence the combined testimony
is to the effect that currents producing the diurnal variation lie
outside.
What is the physical cause of the residual field, or, in other words,
what is the physical cause of the so-called unsymmetrical distribution
of the earth's magnetism f
Shortly after the presentation of the foregoing paper, I finally
found a clue which appears a promising one for the solution
of this problem. Many investigators have surmised that the distri-
bution of land and water has considerable to do with the unsym-
metrical magnetic distribution, but the difficulty has been to prove
it. The reason for previous failures is to be ascribed to the fact
that the arguments were based upon the total magnetic effects. No
attempt has been made to separate from the total field all that portion
which could be referred to a distinct physical cause — for example,
1 Ampere's rule : " Place the outstretched right hand over or under the wire car-
rying the current (always allowing the wire to come between the hand and the
needle), with the palm toward the needle, and the extended thumb in the same
direction as the N-pole of the needle is deflected : then the fingers will point in the
direction the current is flowing."
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f
DECOMPOSITION OF EARTH'S MAGNETIC FIELD
51
that of a uniform magnetization about some diameter, such as we
would have were the earth entirely uniform in its structure. But
even when this separation is undertaken, the residual field does not
at first glance reveal the precise effect of the distribution of land
and water. I recall a remark made by Schuster, in which he ex-
pressed his disappointment that my preliminary chart 1 did not
exhibit any relationship to the distribution of land and water.
On the next plate is reproduced the chart of isabnormal temper-
ature lines, as given in Hann's Atlas der Meteorologie. Compare
this chart with that of the residual magnetic field opposite page — ,
and a striking similarity will at once make itself manifest. Follow
out, for example, the zero line skirting at first along the northeast
coast of North America and then cutting across Africa, or the one
between Europe and Asia. Note that in those regions of the North-
ern Hemisphere where the annual temperature is less than the
normal temperature, 2 /. e. t in the relatively cold regions, north-
eastern Asia and eastern North America, the north end of the dip
needle is attracted or the south end repelled. In these regions, we
have the secondary north magnetic poles. In the warm regions,
on the other hand, central and eastern Africa, Europe, the Aleutian
Islands, and western Asia, the north end of the dip needle is
repelled, or the south end attracted ; here we have the secondary
south magnetic poles.
We even have an analogous state of affairs on the temperature
chart as exhibited by the double foci S x ' and S" of the magnetic
chart. Thus the plus isanomalous or isabnormal temperature lines
inclose two foci, one along the Norwegian coast and the other in
the Arabian desert. Later charts would shift the latter more to-
wards the central part of Africa, agreeing thus better with the
position of 5/.
In the Southern Hemisphere, the condition of things appears to
be the reverse. Thus JV 2 is within the relatively warm region
(east coast of South America) and S 2 , acccording to the later
charts, is in a relatively cold region.
The magnetic effects can be reproduced quite closely, starting
with the isanomalous temperature chart and assuming that the
magnetic power of the earth decreases with increase of tempera-
ture, and increases with decrease of temperature. I have amused
myself with such attempts, and have reproduced qualitatively,
J The one reproduced in the Journal, October, 1896. It will be found that this
chart showed the main characteristics of the residual field quite satisfactorily.
* Average temperature along a parallel.
52
L. A. BAUER [vol. iv, No. i.)
the main facts of the residual magnetic field, starting with-
an annual isothermal chart, for example, that by Hahn.
This matter must be reserved, however, for a future num-
ber. Isanomalous temperature charts as based upon the most
recent data will be constructed and carefully studied in connec-
tion with the magnetic map.
If the unsymmetrical distribution of the earth's magnetism is
to be referred principally to the unsymmetrical distribution of
temperature of the earth's crust, then the seat of the earth's
magnetism must be at such a depth below the surface that it will
not be affected by the diurnal and annual variations in tempera-
ture. If the earth's magnetism were spread over a thin layer at
the surface it would suffer a diurnal and an annual variation many
times larger than those actually observed. Furthermore, the di-
urnal and annual variations of the earth's magnetism are to be re-
ferred to causes outside of the earth's crust.
For the present, we will content ourselves with the following
conclusion :
The unsymmetrical distribution of the earth's magnetism and the
unsymmetrical distribution of temperature as exhibited on the earth's sur-
face, on the average for the year, are in some way related to each other.
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IS THE PRINCIPAL SOURCE OF THE SECULAR VARIA-
TION OF THE EARTH'S MAGNETISM WITHIN OR
WITHOUT THE EARTH'S CRUST? 1
By L. A; Bauer.
[Preliminary Communication.']
In the papers on the " Distribution and the Secular Variation
of the Earth's Magnetism," presented before the Washington Phil-
osophical Society in May, 1895, I showed that certain laws per-
taining to the distribution of the magnetic elements over the earth's
surface are similar to those pertaining to the secular variation as
derived thus far. I shall refer to four of the deductions then made,
as they will be found interesting in connection with some of the
conclusions reached in this paper. These laws 9 are:
I. The minimum range in declination along a parallel of latitude occurs
near the equator, generally increasing upon leaving the equator. II. The
maximum range in inclination along a parallel of latitude occurs near the
equator, generally diminishing upon leaving the equator. III. The minimum
average secular change in declination along a parallel of latitude from 1780
to 1885 occurred near the equator, the values generally increasing upon leav-
ing the equator. IV. The maximum average secular change in inclination
along a parallel of latitude from 1780 to 1885 occurred near the equator, the
values generally diminishing upon leaving the equator.
From the paper presented before the same Society on January
21, 1899, it was seen that by far the greatest portion of the per-
manent magnetic field must be referred to sources within the
earth's crust, which fact had already been proven by the researches
of Gauss and of Schmidt. In view of the similarity of the laws
of the distribution and of the secular variation phenomena referred
to above, the question immediately arises : Is the principal part of
the secular variation likewise to be referred to sources within the
earth's crust? Manifestly this question is a practical one — one that
must be solved first before we can successfully take up the next
question— What is the cause of the secular variation?
How shall we undertake the solution of the problem with re-
gard to the location of the source of the secular variation? Gauss,
in his celebrated memoir on the earth's magnetism, elaborated a
mathematical method for the separation of internal and external
sources. Gauss and Schmidt have applied this method success-
1 An abstract of thi9 paper was read for the author by Mr. J. F. Hay ford before
the Washington Philosophical Society, February 4, 1899.
* See American Journal of Science , Vol. L, pp. 113 and 114.
53
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54 L. A. BAUER [Vol. IV, No. i.)
fully to the earth's permanent field, and Schuster has made use of
it in showing that the cause of the diurnal variation is outside of
the earth's crust. Gauss's method, however, involves a knowledge
of the magnetic intensity, while in the discussion of the secular
variation we are restricted to changes of declination and inclina-
tion, the intensity data reaching over but half a century, being as
yet not sufficient. Evidently, then, we must use another method
if we wish to take into account the secular variation changes of
the past three centuries. We solve the problem with the aid of
the following proposition :
If the observed changes in the compass and in the dip needle
can be completely accounted for by hypothetical causes within the
earth's crust, then they can not be produced by causes without the
crust. 1
Let us have concretely before us what we desire to prove. In
my last paper I had resolved the earth's permanent field into two
main portions; the larger portion, representing nearly three-fourths
of the entire field, could be regarded as due to a uniform magnet-
ization about an axis inclined n° 25^.7 to the axis of rotation; the
remaining portion was termed the residual field, and was graphic-
ally represented. This method of decomposition of the permanent
field has been found to be a very useful one, simplifying greatly
the discussion of the complex magnetic phenomena. We employ
precisely the same mode of decomposition in the discussion of the
very complex phenomena of the secular variation.
We shall, then, in the present paper consider simply the secular va-
riation of the uniform magnetic field, which, as stated, represents
nearly three-fourths of the total magnetization. In a future paper
we will discuss the secular variation of the residual field. The axis
of the uniform magnetization is a straight line passing through
the earth's center, and intersecting the surface in two points dia-
metrically opposite each other.
What is the secular motion of the magnetic axis of the uniform
field?
A preliminary solution of this question was presented before
the American Association for the Advancement of Science in 1896.
I have had no time to repeat the computations with the aid of my
more complete data. Selecting the values of the declination and
inclination along the five parallels ±40° ±20° and equator, at the
1 The precise limitations of this proposition will be discussed in the com-
pleted paper.
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SOURCE OF SECULAR VARIATION 55
intersections of meridians 20 apart, we obtain, with the aid of the
formulae developed in our last paper for the geographical co-ordi-
nates of the intersection of the magnetic axis :
Epoch
I,AT.
Long.
W. OF Gr.
1885
8o°.oN
75°4
1780
79 .8 N
56 .2
Change
.2
19 .2
Hence the uniform magnetic field from lySo to 1SS5 has been slid-
ing practically along a parallel of latitude from east to west at the
average rate of ^=o°.i829 longitude per annum, or i."8 per day.
If the uniform field continued to revolve in this way, it would
take 1,970 years, or about 2,006 years, to make a complete rotation,
this period agreeing well with a previous deduction. I quote from
the paper 1 presented to the Washington Philosophical Society in
May, 1895: "For 3^ centuries the lines of no declination have
been moving apparently uniformly along the equator in a westward
direction. If the motion continues at the same rate around the
equator, then the west agonic will accomplish a complete revolu-
tion in 1,580 years, the east agonic in 2,590 years. The average
annual motion of the two agonies is o°.i94, and the average period
of revolution about 2,000 years."
We have, then, this solid fact presented to our minds; viz., that
the chief portion of the earth's permanent magnetism is revolving
slowly but surely from east to west, or contrary to the direction of
the earth's rotation. In other words, the secular variation is prin-
cipally caused by a change in the direction of the magnetic axis.
Does it not follow at once that the source of the secular variation
is an internal one, if the field which revolves is itself to be ascribed
to internal causes?
Or let us examine the matter with the aid of the proposition
proposed at the beginning of this paper. Let us suppose that we are
not acquainted with the fact that the earth's permanent magnetism
is to be referred principally to causes within its crust, and that we
have before us simply the secular variation phenomena. We know
that there is a certain magnetic field sliding around the earth from
east to west, which by reason of its change of position causes a sec-
ular variation. We know, furthermore, that the secular curve de-
scribed by the north end of a freely suspended magnetic needle, as
viewed from the center of the needle, proceeds clockwise over
the greater part of the earth.
*See American Journal of Science, Vol. h, p. 319.
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56 £• A. BAUER [Vol. IV, Na i]
Now, as far as the secukr changes in declination are concerned,
the sliding magnetic system could either be within the earth's crust
or without ; but if at the same time the observed changes in inclina-
tion are to be reproduced, then the moving system must be within
the crust. We find, namely, that an internal magnetic system moving
from east to west will make the secular curve proceed clockwise in
both hemispheres, whereas an external magnetic system moving
westward would cause the secular curve to be described in a direc-
tion contrary to that of the hands of a watch. There are certain sta-
tions in the Pacific Ocean, and on its shores, where we have anti-
clockwise manifestations in the secular curves, and it is quite pos-
sible that, in addition to the moving internal magnetic system, we
have an external system standing in a fixed relation to the internal
one. The investigations of Schuster, Schmidt, and Carlheim-Gyl-
lenskold indicate that there is such an external field. Our first ob-
ject, however, must be to examine the principal moving magnetic
system, and determine, if possible, the source of energy from which
the mechanical work performed in driving the magnetic system
around the earth is derived.
What force on the earth have we, the expenditure of whose en-
ergy has not as yet been strictly accounted for ? Twice in a lunar
day the tidal waves beating against our eastern shores sweep around
the earth from east to west. A complete estimate of the work of
the tides has thus far defied numerical computation. A part of the
tidal energy is consumed doubtless in retarding the earth's rota-
tion, and in supplying the internal heat.
Let us next examine the phenomena of the lunar-diurnal varia-
tion. On the diagram opposite I have drawn for various stations
in both hemispheres the curve described by the north end of a
freely suspended magnetic needle under the influence of the lunar-
diurnal variation of the earth's magnetism. We first notice that
each curve consists of two geometrically similar loops of somewhat
different area, each requiring twelve lunar hours for its completion.
Next we note the very important fact that the general direction of
motion, not only for both loops \ but likewise for all the stations ', whether
in the northern or in the southern hemisphere, is like that of the secu-
lar motion curves — clockwise. Considering the minuteness of the
lunar-diurnal variation, the range in declination and inclination
being but a fraction of a minute, the revelation of this beautiful
and hitherto unsuspected law is a most striking circumstance. We
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SOURCE OF SECULAR VARIATION
57
CURVES DESCRIBED BY NORTH END OF FREE MAGNETIC NEEDLE
LUNAR-DIURNAI, VARIATION SECULAR VARIATION
* n • ? ■ .♦ +
KRIS
[Reproduced from Nature.']
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58 £• A. BAUER [vol. iv, no. i.]
have in the lunar-diurnal variation a secular variation in miniature.
And the remarkable similarity between the two variations holds
still further. It will be seen that the lunar-diurnal variation has its
minimum range in declination and maximum range in inclination
near the equator, atid that these quantities respectively increase and
decrease upon leaving the equator — laws precisely similar to those
quoted at the beginning of the paper as referring to the secular
variation and the distribution phenomena. Note, also, that the
area of the curve for Cape of Good Hope is decidedly larger than
that for Kew, just as is the case with regard to the secular variation.
The phenomena of the distribution of the earth's magnetism, of
the secular variation, and of the lunar-diurnal variation, are pre-
cisely similar, differing simply in range or magnitude.
The curves of the lunar-diurnal variation can be completely re-
produced by supposing the earth's magnetic axis to revolve around
its mean position twice in a lunar day from east to west. It fol-
lows, then, that the cause of the lunar-diurnal variation must like-
wise be referred to a cause within the crust. And as it has been
proven by Lloyd and Stoney that the moon, considered as a mag-
netized body, can not, at its distance, produce the observed magnetic
effects on the earth, it is very probable, as has been repeatedly sur-
mised, that the cause of the variation must be referred to the tidal
strains to which the magnetized earth is subjected twice in a lunar
day. It is, then, an experimentally proven fact that the earth's mag-
netic axis revolves around its mean position in a clockwise direction
twice in a lunar day. Furthermore, at the end of the lunar day
the axis is not in the same place as it was at the beginning of the
day ; for the lunar-diurnal variation does not appear to be a cyclic
phenomenon, the outstanding residual effects being of the order re-
quired for the secular variation. In a future paper a more exhaust-
ive examination of this matter will be undertaken.
Explanatory Remarks. On the diagram, page 57, are the curves described by a
freely suspended magnetic needle under the influence of the lunar diurnal variation
of the earth's magnetism at various stations. The observer is supposed to be stand-
ing at the center of the needle and looking towards its north end. The method of
construction is precisely similar to the one employed in the drawing of the secular
variation curves. In the present case, the formulae are very simple ones : x = d cos /
and y — i , where d and i represent the lunar-diurnal variation in declination and
inclination, respectively, and / the magnetic inclination. The following series of
observations have been used: Toronto (i843-*48), Philadelphia (i84o-'45), Kew
(i859-*64), Batavia (iS&i-'oj), St. Helena (i&tf-^), Cape of Good Hope (i843-'46),
Hobarton (i843-*48). There is some uncertainty regarding the inclination variation
for St. Helena as given by Sabine. It would appear as though the signs as given
by him should be reversed.
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TAFELN ZUR GENAHERTEN AUSWERTUNG VON
KUGELFUNCTIONENREIHEN UND IHREN
DIFFERENTIALQUOTIENTEN.
Von Dr. Ad. Schmidt (Goth a).
Im Laufe einer Reihe von Jahren, in denen ich mit Untersu-
chungen iiber das erdmagnetische Potential beschaftigt war, habe
ich Veranlassung gefunden, mir allmahlich eine grossere Zahl von
Hiilfstafeln zur Erleichterung numerischer Rechnungen anzulegen.
Manche davon, so z. B. die hier mitgeteilten, besitzen eine so allge-
meine und vielfache Verwendbarkeit, dass ihre Veroffentlichung
wohl gerechtfertigt erscheint.
Zur Auswertung einer durch eine Kugelfunctionenreihe darge-
stellten Function, z. B. eines Potentials V, giebt es bereits ver-
schiedene Tafeln. Ich selbst habe in dieser Zeitschrift (Vol. I, pag.
75» 76) eine kleine Tabelle der Logarithraen der Functionen R^
mitgeteilt. Diese Hulfsmittel sind indessen noch nicht bequem
genug, wenn man, was oft vorkommt, schnell eine weun auch nur
ganz rohe Uebersicht (am besten in graphischer Darstellung) iiber
die Verteilung der Functionswerte auf der ganzen Kugelflache
gewinnen will. Es geniigen dann sehr stark abgerundete Werte
der Reihencoefficienten und der Kugel functionen. Diese letzteren
findet man nun — auf 3 Decimalstellen angegeben — im ersten Teile
der umstehenden Tabelle. Rundet man sie, was fur den bezeich-
neten Zweck vollkommen ausreicht, auf 2 Decimalen ab, so kann
die Berechnung der Reihe
+(h\ R\+h\ #[+..) sin \+(h\ /? 2 2 +..) sin 2X+..
mit Benutzung des Rechenschiebers oder einer Multiplications-
tabelle sehr schnell und bequem erfolgen.
Dieselbe Tabelle ermoglicht auch die Ableitung der zu diesem
Potential gehorigen verticalen Kraftcomponente Z, vorausgesetzt,
dass jenes nur von inneren oder nur von ausseren Agentien herriihrt.
Man hat dazu eine genau ebenso gebildete Reihe auszuwerten, deren
59
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60 A. SCHMIDT [vol. iv, no. i.]
Coefficienten im ersten Falle — («+I) mal, im zweiten n mal so gross
sind, wie die Coefficienten £-* und ^* der vorstehenden Reihe.
Die zu dem angegebenen Potential gehorigen horizontalen (in die
Kugelflache fallenden) Kraftcomponenten
x= J_. *V % Y = — . —
r d u r sin u dx
erhalt man, wenn man in der fur ( V:r) geltenden Reihe an Stelle von
g m* h m> R m im ersten Falle n Zm> nh m> X m> im zweiten Falle — nh\
ng^, Y^ setzt, worin
X n =-- ^^ Y n = - R "
m n ' du * m n sinu
ist. Die hier eingefuhrten Functionen X^ und Y£ (denen ich den
Factor £ aus denselben Griinden hinzugefugt habe, die mich zur
Einfiihrung der Functionen R^ bewogen) findet man im zweiten
und dritten Teile der Tabelle.
Auf die im Vorhergehenden geschilderte Art erhalt man zu-
nachst die Coefficienten von trigonometrischen Reihen fur eine
Anzahl von Parallelkreisen. (Es wird meistens geniigen, nur die
zu den Werten #=20°, 40 . . . 160 gehorigen Parallelkreise zu
beriicksichtigen.) Man hat nun noch diese Reihen fur eine Anzahl
von aequidistanten Punkten auszuwerten, was leicht in bekannter
Weise geschieht. Am bequemsten ist es im allgemeinen, 24 oder,
was meistens ausreichen wird, 12 solcher Punkte zu wahlen.
Die Bedeutung der Buchstaben ergiebt sich zwar aus den For-
meln, mag aber der Deutlichkeit halber noch ausdriicklich ange-
geben werden. Es ist A die geogr. Lange, 90 — u die geogr. Breite.
Die positive Richtung von X und Y fallt mit derjenigen wachsender
Breite und Lange zusammen ; Z ist nach unten (d. i. nach dem
Innern der Kugel hin) positiv gerechnet ; r endlich bezeichne
den Kugelradius.
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Ort.
ERDMAGNETISCHE BEOBACHTUNGEN IM UMANAKS-FJORD
(NORDWEST-GRONLAND), 1892-93.
Von Dr. H. Stade (Brocken).
Wahrend meines einjahrigen Aufenthaltes im danischeu Nordgronland
gelegentlich der von der Gesellschaft fiir Erdkunde zu Berlin im Friihjahr
1892 dorthin entsandten Forschungs-Expedition, an welcher ich mich als
Meteorologe beteiligte, habe ich im Umanaks-Fjord zwolfmal, und zwar elf-
mal an der von uns gegriindeten Station Karajak und einmal bei der dani-
schen Kolonie Umanak, die absoluten Werte der erdmagnetischen Elemente
(Declination, Inclination, Total-In tensi tat) bestimmt.
Die Beobachtungen zu Karajak wurden samtlich streng an demselben
Punkte und zwar 40 Meter nordlich vom Stationshaus an^estellt ; derselbe
lag in 23 Meter Meereshohe und wurde im N, E und S bis 300 Meter Ent-
fernung von niedrigen Felsen nur wenig iiberragt, wahrend 20 Meter weit im
W ein schroffer Ablall zum Fjord stattfand. Zu Umanak wurden die Beob-
achtungen in etwa 30 Meter Hone etwas westlich von der Kolonie auf einem
die nordliche und ostliche Umgebung ein wenig iiberragenden, nach W und S
steil zum Meere abfallenden Felsen ausgefiihrt. Der Boden, auf dem beide
Beobacbtungspunkte lagen, bestand aus Gneiss, ebenso wie die nahere und
weitere Umgebung derselben. Neben demselben finden sich andere Gebirgs-
glieder im Umanaks-Fjord nur in ganz untergeordneter Ausdehnung und fern
von den beiden genannten Punkten.
Die geographischen Positionen der beiden Stationen sind :
Karajak 70 26' 52" N. Br., 309 5</ 15" E. v. Gr.
Umanak 70 40 36 " " , 308 1 30 " " " .
Zur Messung der Inclination und Total -In ten si tat diente ein Fox'scher
Apparat von Dover in London, zur Bestimmung der Deklination ein berg-
mannischer Azimuthal-Kompass von Meissner in Berlin und zweimal gleich-
zeitig ein kompensierter Poiar-Kompass von Thomas Whiston in London.
Die Beschreibung des Fox'schen Apparates, sowie der von mir ange-
wandten Beobachtungs- und Reductions- Me thoden findet sich in dem " Hand-
buch der Nautischen Instrumente" (herausgegeben vom Reichs-Mariue-Amt,
Berlin, E. S. Mitter, 1890, 2. Auflage, S. 275-297), welches auch zwei Abbil-
dungen des Apparates enthalt ; die ausfiihrlichen Beobachtungen selbst sind
in dem Reisewerk " Gronland-Expedition der Gesellschaft fur Erdkunde zu
Berlin 1891-1893" (Berlin, W. H. Kiihl, 1897, II. Band, S. 391-412) veroffentlicht,
so dass es hier geniigt, eine Zusammenstellung der Resultate zu geben.
Zusatnmenstellung der endgiltigen Ergebnisse.
Datum.
Karajak
1892, Oct.
" Dec.
1893, Jan.
Febr.
Umanak ;
i
3 3 X-4 l /zP
6X-7P
6K-7KP
n#a-ip
5X-6P
Marz 29.
April 15J 5&-6%P
Mai
Juni
Juli_
Aug. 16. 2%-2>%v
18. 1
5-
24.
26.
5 -5KP
7 -7^P
5 SViV
1 -i#a
I
Incli-
nation.
Datum.
8i°59'
82 1
81 37
82 18
82 10
82 2
82 8
82 1
82 o
82 o
82 11
Zcit.
Total-
Inten-
sitat.i
1892, Oct. 16. 5X-5KP
1893, Marz 29. 7 ~7>£p
" April 15 7 -7>^p
44 Mai 18. 6^-6^p
Juni 5. S>£-8^p
5.625 1 1 1892, Oct 5.
5.603 1 44 " 16.
1893, Febr. 5-
Marz 29.
Zeit.
I
Decli-
nation
Juli
24.
26.
6#-6#p
2X~2^a
5.689
5455
5.642
5437
5556
April 15.
Juni 5.
" 24.
Juli 26.
3P 65 o^
2^p 65 26
3#P 65 39
7#P 66 32
7#P 66 26
9HV 65 8
6#p 65 17
2#a 65 41 :
Aug. 16. 3/2-3Up\ 5.617 I
^' 26. 2#a 65 y\
Aug. 1 6.i ip ,62 48 *
i6.!ip 62 54 5
1 Gauss'sche Einheiten.
8 Mit Meissner'schem Kompass.
62
8 Mit Polar-Kompas-
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ABSTRACTS AND REVIEWS
ON THE RELATION BETWEEN THE PHENOMENA OF THE EARTH'S
MAGNETISM AND THE ELECTRIC PHENOMENA
OF THE ATMOSPHERE. 1
Dr. Trabert makes the interesting attempt to establish a connection be-
tween the results of recent investigations in terrestrial magnetism and the
views to which we have been led by the latest observations in atmospheric
electricity.
According to Schmidt's analysis, a small fraction of the earth's magnetic
force must be referred to forces which do not possess a potential, and which
can be regarded as resulting from vertical currents passing through the
earth's surface. Their existence would be revealed if a value differing from
zero expressed the sum total of the work done in moving a unit magnetic
pole around a closed curve on the earth's surface, against the horizontal mag-
netic force. For the entire surface the average values of the current intensity
of the vertical currents amounted to 1.7X10""" ampere per sq. cm. The
investigations of Carlbeim, Gyllenskold, Riicker, von Bezold, and Liznar,
extending over limited regions of the earth, have not revealed the existence
of vertical currents, the values of the work integral being very close to zero.
Their non-existence, however, can not be regarded as definitely proven in this
way, because the smaller the region, the more difficult the experimental de-
termination of the value of the integral.
A computation of the value of the work integral for various parallels from
60 N. to 60 S. has been made by Bauer with the aid of Petersen's values of
the north, east and vertical components of the earth's magnetic force, as fur-
nished him by Schmidt. This investigation revealed a characteristic systematic
variation of the integral with latitude.* It was found that the direction of the
hypothetical earth- air currents was an upward one in the equatorial regions, a
downward one in the lower latitudes, and then upward again at latitude 55°
This distribution, which is analogous to that of the atmospheric pressure, and
to that of other meteorological elements connected with the atmosphere,
speaks for the real existence of Bauer's result.
In his magnetic survey of Austria, Liznar has recently made a determina-
tion of the dependence of the magnetic components upon altitude of station,
and has found evidences that a part of the magnetic force comes from the
lower regions of the atmosphere. If this effect be due to electric currents,
it follows that, over the region explored by Liznar, there are two systems; in
the one, the currents pass from west to east, and in the other, from north to
south. This last result agrees with Bauer's electric circulation ; the upward
1 Trabert, H. Der Zusatnmenhang zwischen den Erscheinungen des Erdmag-
netismus und den elektrischen Vorgangen in der Atmosphare. Meteorologische
Zeit$thrift % November, 1899.
* Terrestrial Magnetism, Vol. II, p. 11, 1897.
63
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64 REVIEWS [vol. iv, no. .]
currents of the high latitudes and the downward ones of the low latitudes,
since we must have closed currents, require in the intervening regions north-
south currents. We must also assume in the northern hemisphere a reversal
of the current direction between the tropic zone and the middle latitudes.
The question now is % how can the conclusions drawn from the magnetic
behavior of the atmosphere be brought into harmony with its known electric
phenomena f
The potential of atmospheric electricity, being in general positive, neces-
sitates the conclusion that the earth's surface is negatively charged ; the de-
crease almost to zero of the field intensity with increasing altitude shows that
the complementary quantity of positive electricity must be distributed in the
atmosphere. Now, electrical movements in the air will result, on the one
hand, from a readjustment of the electric charges on the earth and in the air,
and, on the other hand, there must take place a continuous return of the
electricity escaped into the air, in order that the stationary condition may
result, which we actually observe. In general, the first result will ensue
especially in regions exposed to excessive solar radiation ; i. e., where we have
inferior cloud formation and high temperature, as here the dissipation of the
negative electricity of the earth is promoted. The second restorative move-
ment, on the other hand, takes place rather in the zones where cloud forma-
tion and rainfall preponderate. Hence, in the rain-belt of the calms and in
the two belts of superior cloud formation, in about 6o° latitude, we have
a transference of negative electricity from the atmosphere to the earth —
i. e. t upward currents— and in the two zones of inferior cloud formation, in
the lower latitudes, we have a transference of positive electricity from the
atmosphere to the earth ; i. e. $ downward currents. It will be recognized that
this current system is similar in its character to that found by Bauer.
At this point the author refers to the paper published by Bister and the
reviewer in the Journal (Vol. Ill, p. 49). We pointed out that it must be pos-
sible to determine the direction of a vertical transference of electricity in
the atmosphere, if this transference can be referred to a process analogous
to that of conduction, by the sign of the" potential of atmospheric elec-
tricity, as in this case the current direction is determined by that of the
electrostatic field. An electrical transfer opposed to the forces of this field is
only possible with an expenditure of energy ; we recognize such a case, of a
purely mechanical nature, in the transference of negatively charged raindrops
to the uniformly electrified earth at the expense of the kinetic energy of the
fall. As long, then, as we assume the existence of a generally prevailing
positive potential, the system of electric currents above outlined necessarily
demands such transferences of electricity, either in a purely mechanical man-
ner or in some as yet unknown way.
The quantitative comparison of the results reached from the two different
lines of thought (terrestrial magnetism and atmospheric electricity) is carried
out, assuming that the mean fall of potential is 130 volts per meter. From
this follows a surface density of electricity on the earth's surface of 11X10"" 14
coulomb per sq. cm., whereas the mean intensity of the current passing
through the same surface element, as already given, is 1.7X10"" " ampere,
which would signify a passing of 1700X10"" I4 coulomb per second through
a sq. cm. of surface. Trabert regards this result as surprising, yet within the
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REVIEWS
65
the limits of possibility. The reviewer, however, can not agree with him here.
For the physical interpretation of the result would be, that, for very small sur-
face densities, the dispersion of electricity from the earth into the atmosphere
reaches a value greatly in excess of that which is observed at greater surface
densities. Thus, Linss, 1 by direct measurement, found the dispersion coeffi-
cient of electricity in the free atmosphere to be 0.01 per minute. From this
it follows that, in 100 minutes, the electric charge of the earth's surface
remaining constant, a quantity of electricity escapes into the air which ap-
proaches the amount covering the earth at any moment. More plausible,
doubtless, would be the assumption that the adopted intensity of the earth-air
electric currents has been estimated too high.
Entirely unsuccessful, as is emphasized by Trabert, must be the attempt
to account for east-west electric currents in the atmosphere by mechanical
transfer, as in this case the requisite current intensities would be much
larger.
In any case Trabert's paper deserves to receive the greatest attention from
magneticians and electricians. The magneticians should give us a reliable
determination of the order of magnitude of the intensity of the earth-air
currents, and the electricians should furnish the material for determining the
conductivity of the free air and its relation to other meteorological elements.
Linss's cited paper is the only one bearing on this subject, although the
matter is of such prime importance for a theory of atmospheric electricity.
Recent investigations' have shown that air made conducting by ionization, on
account of the unequal velocity of the oppositely charged ions, gives off free
negative electricity to conducting bodies with which it comes in contact, and
thus develops an electromotive force precisely in the sense required for the
maintenance of the stationary electric condition of the earth's surface. 8
H. Geitei^
Lemstrom and Biese. Observations faites aux stations de Sodankyla et de
Kultala. Electricity attnospherique, courants telluriques> courant ilec-
trique de V atmosphere, ph&nomtnes lutnineux de Vaurore, dorSa/e, naturels
et artificiels. Helsingfors, 1898. 10 x13 cm. Pp. IX-f 26-1-50+98-1-30-1-34.
16 plates.
The work which is here presented to the scientific world has been delayed
by causes beyond the control of the authors. Poor health which had its origin
in the exposure incident to a circumpolar expedition prevented Professor Lem-
strom from attempting more than his regular courses at the University of
Helsingfors.
The observations of the circumpolar expeditions were divided into two
classes: those which were obligatory and those which were optional. The
first-named observations of the Finnish Expedition were published in two
volumes in 1886-7, embracing Meteorology and Terrestrial Magnetism. The
present volume treats of Atmospheric Electricity ; Earth Currents ; Air Cur-
rents (Electrical) and Auroral Phenomena.
The observations of atmospheric electricity began on September 4, 1882.
The instrumental outfit consisted of a Thomson quadrant electrometer as
1 Linss, W. Meteorolog. Z. S., 1887, p. 354, and EUctrotech. Z. S., 1890. Heft 38.
2 Zeleny, Phil, Mag., July, 1898, and Rutherford, Phil. Mag., January, 1898.
The review was translated for the Journal.
9
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66 RE VIE WS i vol. i v, no. i j
modified by Mascart; the distance between the mirror and scale being 1.72
meters. A Thomson water collector mounted upon three insulators was used.
The length of the tube from which the water ran was 2.5 meters, and the
height above the ground 3 meters The electrometer was calibrated by
means of five Leclanch€ cells and the electromotive force determined by com-
parison with a standard Daniel (1.124 volt). During 1882-3, observations
were made each hour, but during 1883-4 oa ^Y three times a day, except on
" term " days when they were made more frequently. Owing to low tempera-
tures and impurities in the water a copper wire ring, with the mesh soaked
in coal- oil, was used as a collector at Kultala. The authors are convinced that
the results thus obtained did not differ materially from those with the other
collector. Frequently the potential values were so large as to pass beyond
the scale limits.
Considering the observations of two years at Sodankyla it appears
that the potential was generally positive and rarely negative. Negative val-
ues occurred during the first year only three times, and only five times dur-
ing the second year. The greatest negative values were observed during
warm weather, as shown in the following table, where the values in volts of
the negative potential are given :
Sept. Oct. Nov. Dec Jan. Feb. Mar. Apr. May June July Aug.
1882-3 . .1492.7 518.6 104.9 93.5 31.3 659.2 184 181.0 2456.6 5130.2 1166.8 1509.0
1883-4 . . 296.8 59.2 97 7 5.7 15.3 6.3 12.3 7.1 121.2 215.Q 172.8 67
Dividing the sums given above by the monthly means as given below, it will
be seen that negative values during both years were most frequent during warm
weather, and that a marked increase is shown with the approach of summer.
1882-3 .
1883-4 .
Sept.
• 30.7
• 52-3
Oct.
46.6
509
Nov.
45-8
22.4
Dec.
45-9
19.8
Jan.
00.9
42 1
Feb.
86.5
18.5
Mar.
96.1
28.3
Apr.
100.9
42.5
May
1206
293
June
60.2
9.2
July
34-4
14.7
Aug
503
1.0
1882-3 .
1883-4 .
Sept.
. 48.6
• 5-7
Oct.
11. 2
1.2
Nov.
2-3
4-4
Dec.
2.1
0.4
Jan.
05
0.4
Feb.
7-7
04
Mar.
0.2
0.4
Apr.
1.8
0.2
May
20.4
4.2
June
852
235
July
Aug.
30.0
6.7
One might naturally expect to find, both in the daily and annual temper-
ature curves, an inverse relation to the curves of electrification. But no such
relationship was found in these observations. Nor is any definite relation
apparent when the observations are grouped by seasons. In order to throw
some light upon the relation of temperature and electricity, Profesor Lem-
stroin divided the observations into two equal groups, one comprising all the
observations made during the warm hours, and the other, those made during
cold hours.
The following table shows the results :
Autumn Winter Spring Summer Year
Warm Cold Warm Cold Warm Cold Warm Cold Warm Cold
499.0 4S4.8 837.7 720.1 2364.2 1 169.9 578.7 580.0 823.3 735-4
The relations of the values of potential with humidity, rain, clear and
cloudy weather, are also discussed ; but, on the whole, these are not so strongly
marked as might have been expected. During summer and autumn the
curves are, for the most part, opposed to each other ; but during winter and
spring there would seem to be an agreement.
Comparing the observations made at the two stations — Sodankyla and
Kultala — a distinct agreement was found to exist in the main. At times of
great variations, however, there would be differences in values. The sign
was nearly always the same. A. McAdie.
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REVIEWS 67
ON THE THEORY OF COMPASS DEVIATIONS. 1
The theory of the deviation of the compasses of ships was first given
by Poisson in 1824, and published in the 5th volume of the Memoirs of the
Institute of France. In a subsequent memoir printed in the 16th volume,
" Sur les deviations de la boussole produites par le fer des vaisseaux," Poisson
put the formulae into such a shape that, after some further modification by
Archibald Smith, they are now the fundamental formulae of the " Deviation
Theory," as the theory of compass errors in iron ships is often called.
In Poisson's treatment, the length of the needle was assumed to be
infinitesimal compared to the distance of the nearest iron ; and on this hy-
pothesis, his equations are exact The immense masses of iron in modern
ships, however, especially in war ships, has made necessary a more or less
complete initial compensation of the compass deviations, by magnets and
soft iron placed in, or very close to, the binnacles carrying the compasses.
This compels a consideration of the lengths of the compass needles, and
possibly also their inductive action on the soft iron masses placed near to
correct them.
That the abandonment of the supposition of an infinitely small needle
would in some iron vessels lead to deviations of a higher order than the
semicircular and quadrantal ones; viz., to sextantal, or even octantal
terms, was pointed out by Dr. Eylert, in No. 3, 1884, of "Aus dem Archiv der
Deutschen Seewarte," and also by Dr. G. Neumayer, Director of the German
Naval Observatory, in his " Handbuch fur Fiihrer von eisernen Schiffen,"
Hamburg, 1889.
An example was given by Dr. Eylert of the steamship Baumwall, and by
Dr. Neumayer of the steam cruiser Irene y where it would be necessary to con-
sider these higher terms of the deviation in order to get satisfactory agreement
with the deviations actually observed. No one before Dr. Borgen, however,
seems to have started out with an entirely independent and general discussion
of the deviation theory, in which no limiting suppositions shall be made as
regards the length of the deviated needle, or the distance, position, or orien-
tation, of the disturbing masses which produce the deviations.
This general treatment leads to nine expressions for the components of
force on the compass needle ; viz., three each, in x> y, and r, including in their
development a total of 108 separate terms. Fortunately, however, each of
these long expressions — every single term a function of the distances involved,
the possibly oblique angles of position of the deflecting magnets, compass
course of the ship, etc. — is reducible to the same general form, viz. :
--im-\-m x sin 2 Z + *n t cos 2 £ 1.
M is the magnetic moment of the deflector, e is distance from center of
needle, and K is compass course. The w's are constants, and contain as
1 Borgen, C. Zur Lehre von der Deviation des Kompasses. Ableitung des
Ausdrucks fiir die Schwingungsdauer einer unter dem Einflusse eines beliebig
gelegenen Magnets stehenden Nadel.
Aus dem Archiv der Deutschen Seewarte. Dr. G. Neumayer, Direktor, Ham-
burg, 1897. Herausgegeben von der Direktion der Seewarte.
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68 • RE VIE WS [Vol. IV, No. i . 1
factor the square of the ratio of the magnetic length, or pole distance, as
it may be termed, of the needle, to the distance of the disturbing magnet
In Poisson's treatment, this ratio is expressly taken as vanishingly small,
and a correspondingly great reduction of complexity — but also of generality —
is thereby brought about. The final outcome of Dr. Borgen's treatment is
the establishment of three equations similar to Poisson's, and but only a trifle
more complex. They, in fact, contain only two columns more than the equa-
tions of Poisson, and the terms of these columns are linear in x, v, z. On
giving to the usual coefficients of the deviation a slightly extended significa-
tion in terms of the coefficients of the new, or extended Poisson coefficients,
an expre*sion for the sine of the deviation is obtained, exactly similar in form
to the one heretofore used in the deviation theory.
In addition to the common five coefficients, Saxon A, B, C, D, E, there are
in this formula six more, thus allowing for possible sextantal and octantal
deviations. It is pointed out by Dr. Borgen that the sextantal errors can not
be corrected by the same magnets as are used for the semicircular ones,
because the square of the ratio of needle length to magnet distance is an
entirely different ratio for the compensating magnets and the ship's iron.
The coefficients of the sextantal deviation are of such a form that, when the
disturbing magnet has its center under the center of the compass-rose,
# = o, and the coefficients disappear. 1 So compensation of this particular
form of deviation must be effected by magnets eccentrically placed.
These must, however, be symmetrically placed upon opposite sides of the
compass needle, and can be either horizontal or vertical ; if vertical, to avoid
heeling error, placed on the compass bowl itself; if horizontal, they must be
put in the plane of the needle.
Dr. Borgen shows that while the use of compensation magnets to correct
the sextantal deviation brings about a large change of the previously existing
semicircular deviation, still that, so far as present experience shows, this
effect is opposite in sign to that already existing, and so tends to diminish it,
or reverse it altogether.
Tables are formed to show that both the sextantal and this remaining
semicircular deviation, whatever it may happen to be, can be fully compen-
sated ; but as the whole procedure is somewhat laborious, it is, on the whole,
best [as seems to be the practice in the American navy] to avoid so far as pos-
sible any necessity for this compensation, by using the shortest possible
needles, having them placed near the center of the compass card, and, of
course, symmetrically placed on opposite sides in respect to the jewel and pin.
[In "binnacle type V" of the American navy, a couple of soft iron bolts are
used as quadrantal correctors, whose power " is principally due to induction
from the compass needles."]
A treatment of the generalized value of \ follows [// a, denotes the mod-
ified horizontal force on shipboard, a, being generally less than unity, for
most ships, about 0.8 or 0.9]; in which it is shown that the directional force
on board is modified by ihe disturbing masses of iron and steel in a much
larger measure than the direction itself, inasmuch as the ratio of the squares
of the oscillation periods of the needle on board and on shore has certain
coefficients in it which are three times as large as in the similar expression
1 a is the projection on the horizontal plane of the distance e.
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REVIEWS 69
for the deviation only. As a consequence, the oscillations for intensity ought
[where sextantal and octantal deviations exist] to be carried out, not with a
small needle, as is usually done, but, if possible, with the compass-card itself,
both on shore and shipboard. This is because the ratio — 7- is wholly different
for the compass needles, and the short needles of the intensity apparatus.
For a final comparison of the general theory of compass deviations on
board ship, discussed in this paper, with magnetic attractions in general, an
expression is worked out for the angle of deviation, and the period of oscilla-
tion, of a needle acted on by magnets placed in any relative positions what-
ever, except that the needle can rotate only in a horizontal plane. The devel-
opments are carried out to the inverse seventh power of the distance, and
of course become the common expressions of Gauss and Lamont, when the
corresponding simplifications are introduced. A paper on this subject has
been already published by Dr. Borgen in " Terrestrial Magnetism," Vol. I, p.
176, in which one development is carried so far as the inverse thirteenth
power of the distance. The author therein shows briefly also the effect of the
bodily dimensions of the deflecting magnets. He has elsewhere written a
special investigation upon this latter correction. John E. Da vies.
University of Wisconsin, February 10, 1899.
PROFESSOR WILD'S PLAN OF A MAGNETIC OBSERVATORY. 1
This paper contains a carefully worked out plan, in full detail, for a
magnetic observatory. Ample provision is made in one cross-shaped, surface
building, 24 meters long, average width 10 meters, and height 5 meters, for
the absolute instruments and two sets of variation instruments, the one self-
registering, and the other for eye-readings. The room containing these
instruments is isolated from the exterior walls of the building by a corridor
which can be suitably heated, and is lighted from above and from the side.
The fundamental idea of the author's plan is a twofold one : (1) All instru-
ments shall be ever ready for immediate use ; t. e., the magnets shall always
remain mounted in the instruments to which they belong. (2) The same
observer shall be able to make, not only the absolute observations, but also
the accompanying differential ones.
The selected dimensions of the building make it possible to dispose the
various instruments in such a way that the mounted magnets, as the author
shows, will not exercise a disturbing influence upon each other; hence the
first requirement can be readily fulfilled. So also the second requirement
can be easily carried out, yet the advantage of the arrangement is question-
able in certain cases. For not only will it increase the time required for a
complete set of observations, but will also decrease the accuracy of the variation
observations even *n middle latitudes, since it is impossible to make both sets of
observations strictly simultaneous in the case of the vibration observations.
If a second observer is not at hand, the reviewer thinks that Schering's scale-
1 Wild H. Ueber die Enrichtung erdmagneti9cher Observatorien. Bull, de
V Academic Imperiale des Sciences de St. Petersburg-. 1898. Mars t. VIII, No. 3.
Pp. 191-206. One plate. 21x30 cm.
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yo RE vie WS rvou iv, no. i j
photographic method, whereby, upon a given signal or clock contact, the
precise positions of the variation magnets are taken photographically, should
be used. This method is especially recommended at polar stations, where, on
account of moisture, the bromide-silver paper for registration is not well
adapted.
The author's plan is based upon his many years of experience, and is excel-
lently thought out The reviewer, however, would be inclined to adopt the
plan only in such cases where, for economical reasons, it is not possible to
have more buildings. In comparison to the large means which the science of
astronomy requires for its prosecution, the demands of terrestrial magnetism
are certainly very modest, so that a slight increase in the cost by the erection
of more complicated buildings is as yet a matter of little moment
Since it must be considered essential for a complete magnetic observatory
to have a duplicate set of instruments, both of variation and of absolute
instruments, and each set preferably of a different construction, one room for
all the instruments will certainly be found too small, and it may, therefore,
be better in general to adopt the idea of two buildings, as heretofore. Our
experience at Potsdam has clearly shown the possibility of keeping the under-
ground room for the variation instruments dry and uniform in temperature.
The plan, however, of having the room for the absolute instruments directly
overhead has not proven to the best advantage. We have, therefore, recently
erected a separate building, of three rooms, at some distance away. Each room
can be brought to a different temperature, which will be found useful for the
determination of temperature coefficients.
A practical arrangement which the reviewer would like to suggest is as
follows: Two separate buildings, one above ground (for the absolute instru-
ments), the other, distant about 15 meters underground (for the variation
instruments), and connected with the former by a covered passageway. Each
instrument should ha\e a definite place, just as the author proposes. A third
building, at a greater distance away, should be erected for special investiga-
tions, in which larger magnets might be employed. 1 M. Eschenhagkn.
Potsdam.
Baracchi, P., Presidential Address delivered before Section A (Astronomy
and Physics) of the Australasian Association for the Advancement of
Science, Sydney session, 1898. Pp. 20. [With his accustomed enthusiasm,
the author, in this address, points out the great importance of actively
prosecuting magnetic work in the Australasian colonies. From his letter
(cf. p. 72) it will be seen that his efforts have not been in vain.]
Drehar, E., and Jordan, K. F. Untersuchungen iiber die Theorie des
Magnetismus, den Erdmagnetismus und das Nordlicht Berlin, Springer,
1898. 8°. Pp. 18. Price, 60 Pfenuige.
Greenwich. Results of the magnetical and meteorological observations
made at the Royal Observatory, Greenwich, in the year 1895. Under the
direction of W. H. M. Christie. London. 1897. 4 . Pp. xli -f cxi. 7 plates.
1 The review was translated for the Journal.
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NOTES
PROFESSOR ARTHUR W. RUCKER, Sec. R. S.
We begin our series of portraits of eminent magneticians with that
of the President of the Permanent Committee on Terrestrial Magnetism
and Atmospheric Electricity of the International Meteorological Confer-
ence, Professor Arthur W. Riicker, Sec. R. S.
Professor Riicker is the eldest son of the late D. H. Rucker, of Clap-
ham Park, London; he was born October 23, 1848. His family, though
of German origin, has been settled in England since 1760. He was ed-
ucated at the Clapham Grammar School and at Brasenose College, Ox-
ford. At the University he gained first classes both in mathematics and
in natural science, and was elected Fellow and Mathematical Lecturer of
his college and Demonstrator in Physics in the University Laboratory.
In 1874 he was appointed Professor of Mathematics and Physics in the
then newly-founded Yorkshire College, Leeds. There he worked for
eleven years, taking an active part in the organization of the college
and in the foundation of the Victoria University, in which the colleges
of Manchester, Liverpool, and Leeds are now included.
In 1885 he was invited to stand as a candidate for Parliament for
the northern division of Leeds, but was not successful in the election
which followed. Returning to his scientific work, Professor Rucker was,
in 1886, appointed Professor of Physics in the Royal College of Science,
South Kensington. This post he still holds. Since settling in London
he has taken an active part in the work of the University of London, of
which he is a Fellow, and in that of various scientific societies. He has
been president of the Physical Society of London, treasurer of the British
Association, and is now, in succession to Lord Rayleigh, secretary of the
Royal Society.
Professor Rucker has written on many scientific subjects. In con-
junction with Professor Reinold, F. R. S., he published, in the Philo-
sophical Transactions, a series of papers on the properties of liquid films.
He has also written on the dynamo, on combination tones, on the theory
of dimensions, on magnetic shielding, on thermometry, and other topics.
Among those interested in terrestrial magnetism, he is known for an
elaborate magnetic survey of the United Kingdom, carried out by him-
self and Dr. Thorpe, F. R. S. In connection with this undertaking, he
has studied the magnetic permeability of basaltic rocks, the causes of
local magnetic disturbances, and the existence of earth-air electric cur-
rents. This work has been published in the Philosophical Transactions
for 1890 and 1896, and ranks among the classics in terrestrial magnetism.
In recognition of these investigations, he was elected a Fellow of the
Royal Society in 1884, and awarded a Royal Medal in 189 1. He was ap-
pointed President of the Permanent Magnetic Committee in 1896.
7i
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72 XOTES (vol. iv, no. i.]
ACTIVITY IN MAGNETIC WORK.
One must be in charge of the Journal to adequately appreciate the
wonderful activity that i9 being manifested in every quarter of the globe in
the study of the magnetic and electric phenomena of the earth and the air.
Scarcely a day passes which does not bring us something of interest, either
in the form of a letter, a MS., a publication, a letter of inquiry, a call far back
volumes, or a new subscription. In the present number we can only mention
a few of the items which our correspondents have kindly sent to us. The
proper acknowledgment and characterization of the many valuable publica-
tions received must be reserved for the next issue.
Magnetic Work in the United States. State surveys are being carried out in
Maryland, West Virginia, and North Carolina. The Coast and Geodetic Survey is
making preparations for greatly increasing the scope of its work. The magnetic
survey of the country is to be energetically prosecuted, and several magnetic observ-
atories are to be established. The next issue will contain a full account of the pro-
posed work.
Magnetic Survey oj Northern Germany. The plan as detailed in Terrestrial
Magnetism, Vol. II, p. 44, has been begun. In 1897 the three magnetic elements
were observed at 30 stations within a radius of 40 km. from the central observatory
at Potsdam, and in 1898 complete observations were made at 45 stations, about 40 km.
apart ; and, in addition, at 8 so-called " primary stations," where more elaborate ob-
servations were carried out. At the primary stations, observations will be repeated
at intervals of a few years for the purpose of determining the secular variation, and
of controlling instrumental corrections in the progress of the work, and to facilitate
the connection of future surveys with the present one. There are to be about 30 of
these stations, and it is hoped that all of these will have been occupied by the end
of this year. To facilitate operations, a second set of survey-instruments is to be
procured. The first part of the summer of 1897 was devoted to the study of electric
car influences. Self-registering instruments were placed at various distances from
the electric tramways, and observations were made simultaneously at Potsdam. The
results will be embodied in a special article. It will be of interest to add that, when
the return current passes through the earth, appreciable effects are felt at a distance
of 8 km.
Magnetic Work in the Australasian Colonies. " The Australasian Association for
the Adv. of Sc, at its Sydney meeting, in 1898, on the recommendation of Section A,
created a committee for the purpose of promoting the study of Terrestrial Magnet-
ism in the Australasian Colonies, and passed a resolution urging the New Zealand
Government, in particular, to establish a permanent magnetic observatory in that
colony, and subsequently to initiate a general magnetic survey. The importance of
such a station is well known, and was pointed out by various leading magneti-
cians, especially by Dr. Adolph Schmidt. The secretary of the committee, Mr. C.
Coleridge Fair, was very energetic and persistent in arousing the New Zealand peo-
ple to take an interest in the matter, and the consequence was that the New Zealand
Government passed a vote of /"500 towards the establishment of a permanent sta-
tion. At present Mr. Farr is making preliminary observations with a set of abso-
lute instruments, very liberally lent to us for two years by the Kew Committee, in
order to ascertain the most suitable locality for the permanent Observatory.
"Another practical result of the 1898 meeting of the Australasian Association for
the Advancement of Science was its recommendation to the Vict >rian Government to
supply means to the Melbourne Observatory for the reduction of the magnetic records
of the last thirty years ; a work of considerable magnitude, which has been found im-
possible hitherto to undertake owing to the smallness of my staff.
" On the strength of the recommendation, we have so far obtained a grant of
/"ioo, and two young computers have been engaged and trained in measuring and
reducing the magnetic curves, and the work is now proceeding. It is hoped that, hav-
ing thus commenced this important work, means may be increased later in order to
deal more efficiently and at a quicker pace, with this great mass of accumulated
material. It is intended to measure all the curves, without distinction between dis-
turbed and quiet days, so that the records may be utilized to their full extent.
" Naturally, the curves corresponding to days on which absolute measurements
were made are being treated first ; and as soon as this part of the work is completed,
I will send you a list of the values of the three elements from 1868 to date." — P.
Baracchi (January 16, 1899).
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[Plate III.]
frbs, .^4.fvCjt~
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Terrestrial Magnetism
and
Atmospheric Electricity
volume IV JUNE, 1899 Number z
THE BEGINNINGS OF MAGNETIC OBSERVATIONS. 1
By G. Heixmann.
After Christopher Columbus discovered the magnetic declina-
tion, on the 13th of September, 1492 — or, as others think, the geo-
graphical variation of the same — mariners began to bestow in-
creased attention on the compass. 2 Voyages to the West Indies
becoming now more frequent, showed that the declination of the
magnetic needle from the astronomical meridian, which on the west
coast of Europe was easterly, decreased gradually toward the west,
vanished in the neighborhood of the Azores, and then passed over
into a westerly declination. What wonder, then, that it was thought
that in this way the geographical longitude could be determined!
Christopher Columbus and Sebastian Cabot had already thought of
the possibility of such a solution of this, the most important of the
nautical problems of that time, and in the sixteenth century the
number of those who sought to ascertain the longitude magnetically
increased very materially. The fact that the line of no declination,.
or the agonic line, almost coincided with the zero meridian as
adopted at that time — at least in that part of the Atlantic Ocean
traversed by voyagers to the West Indies — certainly helped not a
little to continually strengthen the belief in the possibility of de-
1 Translated by Mrs. L. A. Bauer from the original article in the Zeitschri/t der
Geselhch.fiir Erdkunde zu Berlin, Bd. XXXII, Heft 2, with some additions by the
author.
2 Further information, documents, and explanations follow at the close of the
article, but could not be given with the translation.
2
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74 G. HELLMANN [vol. iv, No. a.j
termining the longitude with the aid of the compass. The agonic
line was looked upon as a point of departure given by Nature her-
self for the reckoning of longitude.
While the hope of finally arriving at a correct solution of the
longitude problem was continually and most directly inciting the
mariners of the sixteenth century to observations and speculations
concerning the distribution of magnetic forces over the surface of
the earth, the students on terra firma remained almost altogether
unaffected by these questions. Uninfluenced by the discoveries of
Columbus and his successors, they were led, on the other hand, to a
separate and quite independent discovery of the magnetic declina-
tion. As I will show, it was the construction of sun-dials that first
brought those on land to a true perception of the declination of the
magnetic needle from the astronomical meridian.
Besides fixed sun-dials, the use of which may be traced back
into the Babylonian-Chaldean period, they had also, in olden times,
portable sun-dials for traveling purposes. These were first made,
however, in simple and practical form, after the directive property
of the magnetic needle became known. Then simple horizontal
sun-dials, provided with compasses, were constructed. When and
where this first occurred, I shall not venture to state; but concern-
ing the time of this innovation, so much may at least be said, that
it most probably occurred after the advance had been made from
the water compass to the pivot suspension of the magnetic needle,
hence toward the end of the twelfth century. But whether really
at so early a period such sun-dials were constructed, must remain
undecided, since none have been preserved for us from that time,
nor any written testimony concerning their existence ; though, to
be sure, the astronomical-physical manuscripts, which are buried
in libraries and archives, have not as yet been thoroughly ex-
amined.
The oldest portable sun-dials, which are preserved in the mu-
seums of London, Paris, Dresden, Vienna, Berlin, Nuremberg,
Prague, Darmstadt, and elsewhere, date from the beginning of the
sixteenth century. A large— indeed, perhaps, the larger — portion
of them is of German origin. The reason of this is that Peuer-
bach and his pupil, Regiomontanus, caused gnomonics to be re-
vived, and especially, also, taught the art of constructing portable
sun-dials. Peuerbach, who lectured at the University of Vienna
from 1454-1460, left, besides a pamphlet "Canones Gnomonis cum
nova tabula," a manuscript entitled "Compositio Compassi cum
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FIRST MAGNETIC OBSERVATIONS 75
regula ad omnia climata." At that time, moreover, as I shall soon
show, the word " compassus " meant nothing else than a horizontal
sun-dial, provided with a magnetic needle. From Regiomontanus
also we learn that he constructed such compasses; indeed, accord-
ing to the testimony of J. G. Doppelmayer (" Historische Nachricht
von den Nurnbergischen Mathematicis und Kunstlern," p. 56, note t),
he appears to have been the first to introduce them in Nurem-
berg. In any case, this art found an especially favorable foothold
in Nuremberg (later, also, in Augsburg) ; for the just mentioned
authority gives us, not only the biographies of the noted compass-
makers of Nuremburg — Georg Hartmann, Hieronymus and Paul
Reinman, Hans Troschel and Etzlaub Erhard — but also the fol-
lowing important information, which I shall quote here word for
word (p. 9, Note a) :
44 Die Kunst Kompasse zu machen, wurde nach des Regiomon-
tani Zeiten von mehrern, und dabey sehr lang allein zu Niirnberg,
ausgeubet, desswegen A. 1510 20 Kompassmacher daselbsten bey
einem Hochlobl. Magistrat auch Ansuchung thaten, um ihnen,
wie andern Handwerckern, eine Ordnung furzuschreiben, welche
sie nach ihren Begehren erlanget."
We must conclude from this that, at the beginning of the six-
teenth century, Nuremberg was especially a manufacturing center
for compasses of this kind, which were constructed in such num-
bers that they not only satisfied the requirements of the inland
trade, but were also exported. I shall in fact cite, later, two author-
ities showing that in the first half of the sixteenth century Span-
ish and Portuguese mariners used German sun-dials with magnetic
needle, and indeed, a century later, sun-dials of this kind still passed
in Italy as of German manufacture.
Some might here remark, perhaps, that by a compass-maker at
that time might be understood a circle-maker (maker of pair of di-
viders) or similar mechanician, since the word means also a circle
or pair of compasses in the romance languages. To meet such an
objection, I refer to Grimm's German Dictionary (Vol. V, p. 1685,
Leipzig, 1873), an d add as additional evidence the following two
uses of the word compass. The previously-mentioned Georg Hart-
mann, who, from 15 18 to the end of his life, lived in Nuremberg,
and served as vicar of the Church of St. Sebaldus, possessed an
unusual skill in the making of mathematical instruments, among
which sun-dials occupied a prominent position. He constructed
such sun-dials in great number for princes and persons of high
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76 G. HELLMANN [Vol. iv, No. 2]
rank, among others for Duke Albert of Prussia, with whom he
corresponded. This correspondence has fortunately been preserved
for us (Kgl. Staatsarchiv in Konigsberg) and has been made known
by J. Voigt (Briefwechsel der beriihmtesten Gelehrten des Zeital-
ters der Reformation mit Herzog Albrecht von Preussen. Konigs-
berg 1 84 1. 8°.) From this correspondence it becomes clear be-
yond a doubt that by a compass is to be understood nothing else
than a sun-dial with magnetic needle. In the following manner
writes Hartmann on the 5th of March, 1544, upon sending to the
duke a compass ordered the year previous :
" Gnadigster Fiirst, es kommt die Zeit, dass die Compasse zu .
gebrauchen sind mehr denn im Winter; ich habe deshalb vor einem
Vierteljahr verfertigt acht derselben von Elfenbein, darunter sechs
auf 55 Grad Preussischer Polhohe zugerichtet sind, die andern
zwei auf 54 Grad Polhohe. Auch habe ich gemacht vier kleine
Compassle, alle von Buxbaumstock,auf 55 Grad Polhohe mit meinem
moglichen Fleisse zugerichtet. . . ."
That the Latin word compassus was also used with the same
meaning is proved, for example, by the " Horologiographia," by
Sebastian Miinster (Basileae, 1533. 4 ), in which is found on
page 7: "Verum horarium Mud, quod vulgo compassum vocant, ha-
bens lineae meridianae magneticum indicem, praecellit sua nobilitate et
commoditaie omnes cylindros % anulos. . . ."
The preceding references are certainly sufficient to prove that
at the beginning of the sixteenth century horizontal sun-dials, with
compasses were greatly in vogue and much used. Therefore, it
must often have happened that the deviation in the pointing of the
magnetic needle from the astronomical meridian was observed,
whenever the observer possessed the means or knowledge to de-
termine in some manner the true astronomical meridian.
Such desultory observations alone were not sufficient to shake
the belief, prevailing in the Occident for at least four hundred years,
that the needle pointed true to the pole ; for indeed much later the
deviations of the needle were regarded as imperfections in the con-
struction, or were explained as being due to the various sources
from which were obtained the loadstones used in magnetizing the
needles. However, the thought must soon have come to a man
versed in astronomy, who himself constructed many sun-dials with
compasses and in that connection repeatedly observed that the mag-
netic needle always deviated from the meridian in the same direc-
tion, that therein an obedience to law was concerned. This man
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FIRST MAGNETIC OBSERVATIONS
77
-was the above-mentioned Georg Hartmann, who, during his resi-
dence in Rome, in 15 10, was the first to determine on land the va-
riation of the magnetic needle (6° E.) We discover this from a let-
ter, which he addressed on the 4th of March, 1544, to Count Albert,
of Prussia, in which we read among other things:
"Noch ist an dem Magnetstein dieses grosser zu verwundern,
<Lass die Zungle damit bestrichen nicht gerade laufen der Mitter-
nacht zu, sondern wenden sich ab von der rechten Mittag-oder Mit-
ternachtlinie und kehren sich gegen den Aufgang zu, in etlichen
Landern um 6 Grad, wie ich solches selbst gefunden und gesucht
habe zu der Zeit zu Rom, da E. F. G. Markgraf Gumprecht und
Seiner F. G. Bruder bei einander zu Rom waren; aber hier zu
Niirnberg finde ich, dass solcher Ausschlag ist 10 Grad und von
andern Orten mehr oder minder. Solches wird auch allezeit mit
-einem schwarzen Strichle unter dem Glaslein in den Compassen
angezeigt, welches Strichle, wie man sieht, allwege nicht gerade auf
■die Mitternacht zeigt, sondern lenket sich herum gegen den Auf-
gang."
That we on terra Jirma are indebted to the sun-dial for our ear-
liest knowledge of the magnetic declination, not to the discovery of
Columbus, of which nothing appeared in print, is also clearly set
forth in the well-known Geography of Heinrich Loriti of Glarus,
which appeared first in 1527 (D. Henrici Glareani Poetae Lau-
reati De Geographia Liber Unus. Basileae. 4 ), where we read
on page 9 b :
Figure i
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78 G. HELLMANN [vol. iv, no. 2.j
"In horologiis nostrae aetatis lingnla ilia tremula, quae circumvol-
vitur % lineam meridianam osiendit, quanquam non prorsus ad amussim*
Neque cnim codem meridiano nob i scum , invenitur lapis ille, sed ali-
quant o magis orientali."
As we see from the extract, Glareanus seeks to explain the east-
erly declination of the magnetic needle by the fact that the loadstone
was found under an easterly meridian ; he is thinking, namely, of
the loadstone from Asia Minor or India.
Furthermore, if we look at Fig. i, which is a facsimile reproduc-
tion of the illustration of a horizontal sun-dial with magnetic
Figure 2
needle, which Petrus Apianus gives in his "Cosmographicus Li-
ber" (Landshut. 1524. 4 ), in Col. 51, we must assume an east-
erly declination of about io°. This agrees very well with the state-
ment of Georg Joachim Rheticus to the effect that Apianus had
found a declination of io°, while the text belonging to the illustra-
tion makes no reference to such declination, but assumes that the
direction of the magnetic needle coincides with the meridian line.
This contradiction is hard to explain. Perhaps Apianus regarded
the declination of io° as a peculiarity of his own magnet, not as
one common to all; with this the opinion of Rheticus, expressed
more than twenty years later, would agree.
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FIRST MAGNETIC OBSERVATIONS 79
So, also, we get the oldest known value of the magnetic dec-
lination in Paris from a sun-dial, that Le Monnier (Histoire de
l*Acad£mie Royale de Sciences, Ann6e 1771, p. 29) found in the
collection of Prince de Conti, as we see from the accompanying fac-
simile (Fig. 2) of the drawing there given of this ivory sun-
dial, constructed in 1541 by Hieronymus Bellarmatus. We perceive
from this that the declination of the magnetic needle at Paris, in
1 541, must have been about 7 E.
Besides these observations made with the aid of sun-dials, there
were some other determinations of the magnetic declination in the
first half of the sixteenth century, which were obtained in another
way, or by a method of which we know nothing. There are the
following, ia chronological order :
A Florentine mariner, Piero di Giovanni d'Antonio di Dino,
writes, in January, 15 19, that during a voyage to the East Indies,
he noticed, with great wonder, a change in the magnetic needle ;
beyond Guinea the variation amounted to n^°E. (one point),
and after the passage of the Cape of Good Hope it was westerly.
To about the same time may be referred Tannstetter's observa-
tion of the declination of the magnetic needle in Vienna, concern-
ing which an important document of Georg Joachim Rheticus in-
forms us; for Joh. Georg Tannstetter, of Rhain in Bavaria, was
occupied from 1509 to the end of his life (1530) in Vienna. The
declination at that time amounted to something more than 4 E.
About the year 1530 must have been made the observation of
the magnetic declination on the coast of Palestine, which is graph-
ically represented on Plate V of the work by Jacob Ziegler, Syriae
ad Ptolemaici opens rationem. . . . (Argent. 1532. Fol.)
As A. v. Nordeuskiold has already remarked (Facsimile Atlas,
p. 105 of the English Edition), this must
be the earliest statement of the variation
on a map. If we are willing to regard
the representation (Fig. 3) as reliable,
we have a declination of 25 W., which
seems to be too great. Perhaps it is only
meant that the declination on the coast of
Palestine is westerly.
A determination of the magnetic dec-
p»gure 3 lination as early as the year 1534 is at hand
for Dieppe, which must have been made by one of the two pilots,
Francois of Dieppe, or Crignon. They found io° E., while Ger-
iT * ^W
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8o
G. HELLMANN
[VOL. IV, No. 2.)
hard Mercator, in a letter dated February 23, 1546, gives the dec-
lination in the neighborhood of the Island of Walcheren (perhaps
Flushing) as 9 E.
The declination of more than 13 E., obtained by Georg Joa-
chim Rheticus at Dantzic, must be referred to the year 1539, since
Rheticus accompanied Copernicus in the summer of this year on a
journey from Culm to Dantzic. This observation agrees surpris-
ingly well with the variation for Dantzic, obtained theoretically by
Mercator, and calculated by him to be 14 E.
I give now a brief tabular presentation of the values of the
magnetic decimation in the first half of the sixteenth century
which have thus far become known. In this I shall disregard for
the present the first great series of such determinations, obtained
by Joao de Castro, since I shall speak of these later in greater de-
tail. I shall give here only that value for Lisbon, epoch 1538.
Year
Place
Magnetic
Declination
Observer or Authority
I5IO:b
Rome
6° E
Georg Hartmann.
I5l8:t
Bay of Guinea
liXE
Piero di Giovanni d' Antonio di Dino.
1520^=
Vienna
4 E
Johann Georg Tannstetter. *
1524^
Landshut (Bav.)
10 E
Petrus Apianus (Bienewitz).
1534
, Dieppe
10 E
Francois or Crignon.
1537
Florence
9 E
Mauro (Sphera volgare novaniente tra-
dotta. Venetiai537. 4 . fol. 53*).
1533
Lisbon
7#E
Pedro Nunes or Joao de Castro.
1539
Dantzic
13 E
Georg Joachim Rheticus.
154*
Paris
7 E
Hieronymus Bellarmatus.
*544=t
Nuremberg
10 E
Georg Hartmann.
I546=b
(Is. of Walcheren
9 E
Gerhard Mercator.
Although, therefore, the deviatiou of the magnetic needle from
the astronomical meridian had been confirmed at different places
up to about 1550, it would be very misleading to assume that this
knowledge — at any rate, among scholars — soon became common
property. On the contrary, up to about the end of the sixteenth
century, most of the writers on magnetism and dials made no men-
tion whatever of the decliuation of the magnetic needle.
The reason for this should be sought for in the fact that no con-
temporaneous account of the above-mentioned observations ap-
peared in print which would have contributed to their wider diffu-
sion, as also to the circumstance spoken of above, that the deviation
was regarded simply as a peculiarity of the magnet concerned, but
not of the station, as the documents of Rheticus distinctly show.
Again, these first determinations of the magnetic declination w r ere
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FIRST MAGNETIC OBSER VA TIONS 8 1
subject to a great uncertainty. This, namely, was the case with
the observations made on shipboard, where the imperfect methods,
as well as the frequently poor construction of the compass, were
to blame. The values of the declination obtained by pilots agreed
so poorly with each other — indeed, often directly contradicted each
other — that doubts of the correctness of the magnetic declination
arose everywhere anew, which doubts were most comprehensively
given expression to, in 1545, by Pedro de Medina, in his "Arte de
navegar" (Lib. VI. Cap. III-VI).
The method of the determination of the declination consisted orig-
inally, as the notice in the diary of Columbus of the date Septem-
ber 17, 1492, already shows us, simply in sighting from the compass
to the Pole Star, and thus obtaining the deviation of the magnetic
needle on the disk of the compass. That in this way no great ac-
curacy could be attained is self-evident. It is also to be ques-
tioned whether the movement of Polaris, which describes about
the North Pole a circle of about 5 degrees in diameter, was always
taken into account. Already among the older writers on the mag-
net do we find, namely, an uncertainty in this regard ; at one time
they say that the magnetic needle points always towards the North
Pole ; at another, they assign to it the property of being ever di-
rected toward the Pole Star.
An improvement in the method of determining the declination
at sea was, therefore, a first essential, if the hope, cherished with
so much love and perseverance, of a solution of the longitude
problem by magnetism, was to be realized. An apothecary of Se-
ville, Felipe Guillen, of whom, unfortunately, we know nothing
further, was the one who thought out with this aim a new and bet-
ter method of determining the declination. It is in this connection
interesting to note that the German dials (compasses in the foregoing
meaning of the word) furnished to the Spanish observer, not only
the suitable magnetic needle, but indirectly also the method itself;
for this consisted simply in determining with an arrangement like a
sun-dial with magnetic needle, the magnetic azimuth of the sun at
equal altitudes before and after noon by means of a centrally placed
style or gnomon. The half difference of the azimuths, which were
reckoned from N. through E. to S. and from N. through W. to S.
as far as 180 , was the desired declination of the magnetic needle
from the meridian.
Felipe Guillen, who presented this instrument (brfijula de varia-
cidti) in 1525, to the king of Portugal, Joao III, has unfortunately
3
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82 G. HELLMANN [Vol. iv. No. 2.)
left behind no writing concerning it. He appears to have remained
in Portugal where the instrument was well received. We are in-
debted to the Spanish cosmographer and major pilot, Alonzo de
Santa Cruz, who occupied himself much with the idea of a solu-
tion of the longitude problem by means of the compass, for an
accurate description of the instrument.
The first who made known in print practical methods for the
determination of the magnetic declination was Francisco Falero or
Faleiro, a Portuguese in the service of the Spanish navy, to whom
we owe also the first real text-book on navigation. This work is
so extremely rare that at times its existence has been doubted. It
was never seen even by Martin Fernandez de Navarrete, the learned
author of "Biblioteca maritima espanola" (Madrid, 185 1. 8°. 2
vols., I, p. 459). At present the Biblioteca Nacional in Madrid has
a copy of it. The title runs : " Tratado del Esphera y del arte del
marear; con el regimietode las alturas; coalguas reglas nueuamete
escritas muy necessarias. Con priuilegio ymperial. MDXXXV."
(Seville, Juan Cromberger. 4 , 52 unnumbered folios, Gothic
type.) In the eighth chapter of the second part with the inscrip-
tion " Del nordestear de las agujas," is the matter of the declination
discussed in detail for the first time in print; the author gives three
methods for its determination. These are perhaps designed for the
instrument of Felipe Guillen, but of this no mention occurs any-
where. They consist: 1st. In the azimuth determination of the
magnetic needle at true noon, when the shadow of the style falls
to the north ; 2d. In observation of the shadow azimuths at corre-
sponding sun altitudes before and after noon ; 3d. In observation of
this azimuth at sunrise and sunset.
The permission to print Falero's work was granted on August
18, 1532, but it appears to have been written much sooner; since we
gather from Castanheda's Historia do descobrimento da India, that
an astrologer Faleiro gave to Magalhaes, at the beginning of his
voyage around the world in the year 15 19, a work in thirty chapters,
with the aid of which he could determine the longitude in three
different ways. Now Falero's published work consisted of about
the same number of chapters; namely, thirty-one. This Faleiro
was perhaps Ruy Faleiro, the brother of Francisco, who had orig-
inally formed the plan of this great journey in common with Ma-
galhaes, but later withdrew. Magalhaes wanted to place Francisco
in command of a ship on the condition " que su hermano Rui Falero
cntregase & los oficiales de la rasa y & el su metodo de observar la
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FIRST MAGNETIC OBSERVATIONS 83
longitud de leste-oeste con los regimientos correspondientes" (Na-
varrete, Coleccion IV, p. L). Francisco, however, did not accom-
pany him. Perhaps we have therefore before us in Falero's printed
work the collaborated labor of Ruy and Francisco, and therewith
likewise the knowledge of the Portuguese pilots of the first quar-
ter of the sixteenth century.
Soon afterwards Pedro Nunes, 1 who, in 1537, likewise pointed
out the actual existence of a variation, and emphasized the need of
its determination for nautical purposes, improved the Guillen instru-
ment merely by adding to it a contrivance for the determination of
sun altitudes, and at the same time devised a new method for de-
termining the latitude at any hour of the day. Both methods are
found explained in the very rare writing: "Tratado da Sphera com
a Theorica do Sol e da Lua. E ho primeiro liuro da Geographia
de Claudio Ptolemeo Alexadrino. Tirados novamente do Latim em
lingoagem pello Doutor Pero Nunes, Cosmographo del Rey DO Jo&o
ho terceiro deste nome nosso Senhor. E acrecetados de muitas an-
nota£6es e figuras per que mais facilmente se podem entender. Item
dous tratados que o mesmo Doutor fez sobre a carta de marear.
Em os quaes se decrarlo todas as principaes duuidas de navega£&o.
Co as tauoas do movimento do Sol: e da su declina£ao. E o regi-
meto da altura assi ao meyo dia: como nosoutros tempos" (Lisbon,
German Galharde, 1537; Fol.); to which also as supplement, in
the same year and by the same printer, appeared "Tratado em de-
fensam da carta de marear com o Regimento da altura."
A remarkable opportunity now soon offered itself to prove in a
most comprehensive manner both methods, which were first carefully
tested in 1533 at Evora. The Infant Dom Luiz, who had received
instruction in mathematics and astronomy from Pedro Nunes him-
self, and had shown great interest in all nautical problems, pre-
sented such an instrument to his comrade in study and friend, Jo&o
de Castro, who commanded one of the eleven ships that sailed to
the East Indies in 1538, with the charge to thoroughly test and
examine this instrument as well as the new method of determin-
ing the longitude. Jo&o de Castro, later the fourth viceroy of India,
performed his task most brilliantly. He investigated — to consider
here only the magnetic side of the matter — not only the variation
1 Contrary to the common custom, I write intentionally Nunes, not Nunez, be-
cause, for all who were not Spaniards, there is no reason for following the later Span-
ish custom in writing. In his Portuguese writings this scholar inscribes his name
always Nunes; in the Latin, Nonius.
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84 G. HELLMAXN Ivol. iv, No. 2}
as often as possible, but he made also all kinds of observations
regarding the method itself, concerning the influence of the mag-
netic needle and its magnetization from the obtained value of
the declination, concerning magnetic disturbances, concerning the
deviation of the compass, etc. Indeed, he was also the discoverer
of the magnetism of rocks, of which with us nothing was said before
the seventeenth century. Joao de Castro carried on his observations
also during his voyage along the west coast of India and in the Red
Sea, so that we possess a series of 43 determinations of the dec-
lination between the years 1538-1541 — the first series of this kind
that has come down to us. This remarkable mariner kept very
copious journals concerning all his nautical, magnetic, meteoro-
logical, and hydrographic observations, which contain indisputably
the greatest and most valuable treasure of records of that kind of
the first half of the sixteenth century, and are worthy the zealous
study of all those who intend writing the history of physical geog-
raphy or of navigation during that period. Since I have read
these journals myself, I do not hesitate to pronounce Jo&ode Castro
to be the most important representative of scientific maritime investi-
gations at the end of the epoch of discoveries.
The logbooks, or Roteiros, of Joao de Castro, kept during
the years 1 538-1541, which he sent to his patron, the Infant Dom
Luiz, remained, lying for three centuries as good as unused, in the
archives of Portugal, until they were brought to light and made
known by Nunes de Carvalho, Diogo Kopke, and Jo&o de Andrade
Corvo. Their respective publications are as follows :
/. Roteiro de Lisboa a Goa por D. Jo&o de Castro. Annotado
por Jc4o de Andrade Corvo. Lisbon, 1882. 8°, with charts and
drawings.
2. Primeiro Roteiro da Costa da India desde Goa ate* Dio: Nar-
rando a viagem que fez o Vice-Rei D. Garcia de Noronha em so-
corro desta ultima cidade. 1538-1539. Por Dom Jo£o de Castro,
Governador e Vice-Rei, que depois foi, da India. Segundo MS.
Autographo. Publicado por Diogo Kopke. Porto 1843. 8 °» w *th
portraits and drawings, as well as an atlas of charts and plans.
j. Roteiro em que se contem a viagem que fizeram os Portu-
guezes, no anno de 1541, partindo da nobre cidade de Goa atee
Soez, que he no fim, e stremidade do Mar Roxo. Com o sitio, e
pintura de todo o syno arabico por Dom loam De Castro, decirao
terceiro governador, e quarto viso-rey da India . . . pelo Doutor
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FIRST MAGNETIC OBSERVATIONS 85
Antonio Nunes de Carvalho. . . . Paris, 1833. 8°. With portraits
and a chart, and an atlas of charts and plans.
In order to show the method followed by Joao de Castro, I
give here — as a sample — his first determination of the magnetic
declination made on April 13, 1538, near the island of Madeira:
" Primeira consideracao antes do meo dia
Estando o sol em altura de, 57 graos
ho estilo lancou a sombra, 71 graos
contando do norte pera a banda daloeste.
Segunda consideracao antes do meo dia
Estando o sol em altura de, 61 graos
ho estilo lancou a sombra, 64 graos
contando do norte pera a banda daloeste.
Tendo por esta maneira vereficado a altura do sol a toda a ora, esperei que
depois de meo dia tornasse o sol as duas alturas em que o tomei pela menh&a,
pera me certificar do que fazUo as agulhas no merediano destas ilhas, e
passou desta maneira.
Primeira consideracao depois do meo dia.
Estando o sol em altura de, 61 graos #
ho estilo lancou a sombra, 53 graos
contando do norte pera a banda de leste :
foi logo o arquo dante o meo dia maior que o de depois de meo dia per
esta operac&o 11 graos, os quaes partidos pello meo, fic&o 5 graos }£ t que he
a quantitade que neste lugar a agulha nordestea.
Segunda considerac&o depois do meo dia.
Estando o sol em altura de, 57 graos
ho estilo lancou a sombra, 60 graos
contando do norte pera leste :
foi logo nesta operac&o o arco de depois de meo dia 11 graos, os quaes
partidos pello meo, vir&o d parte 5 graos J4, que he a quantitade que neste
lugar a agulha nordestea."
Both values for the magnetic declination are identical.
The three Roteiros contain detailed records regarding the meas-
urements of the variation. Usually, several determinations of the
azimuth were made before and after noon, those corresponding
with equal sun altitudes were combined; and so also several values
for the variation of the magnetic needle were obtained. These
agree pretty well with each other, since the differences fluctuate
only between o and ^°. We may look upon these differences not
altogether as errors of observation ; for, disregarding other inac-
curacies, those real differences in the value of the variation caused
by the progress of the ship could not be taken into account.
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86 G. HELLMANN [vol. iv, no. 2.}
The method of determining the declination, first tested by Joao
de Castro, soon was universally introduced on ships, and was even
at the end of the sixteenth century recommended anew by mari-
ners and scholars in Spain, England, and Holland. They did not
know that this method was of Spanish-Portuguese origin, and was
already fifty or perhaps a hundred years old. For neither Rio
Riano (1589), nor William Borough (1581), nor Edmund Gunter
(1622), nor Henry Gellibrand (1635), nor, finally, Simon Stevin
(1599), mention the names of Felipe Guillen, Francisco Falero, or
Pedro Nunes. I therefore consider it of importance to make clear
here the true state of things and their connection. 1
1 The greater p ar t f xhe documents alluded to in the preceding pages has been
meanwhile reproduced in facsimile in "Rara Magnetica," No. 10 of Hellmann's
"Neudrucke" (see T. M. % Vol. Ill, 190).
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CARTE MAGNETIQUE DE LA SICILE.
Par M. L. Palazzo.
La carte magn&ique que j'ai l'honneur de presenter aux lecteurs
<iu " Terrestrial Magnetism" a 6ti dress£e d'apres les donn£es re-
cueillies par le Professeur Chistoni et par moi en Sicile, pendant
Y6t6 1890, chacun de nous ayant fait les lev£s magn£tiques dans
la respective partie de territoire assignee par la Direction du Bureau
Central M6t£orologique italien. Les r&ultats de notre relevement
furent jadis publics dans les "Annali" du dit Bureau, et pr6cis6-
ment dans le volume XI, p. 3 e , de la part de M. Chistoni, et dans
le vol. XVIII, p. i e , pour ce qui concernait mon concours. De
plus, un court r£sum£ de la campagne magn£tique de la Sicile fut
aussi insert dans les " Rendiconti della R. Accademia dei Lincei"
(vol. VI, 2 d sem., s£rie 5 e ), oii j'ai ajout£ quelques remarques au
sujet de la particuli&re allure des lignes isomagn£tiques dans les
regions explores.
Mais, comme dans aucune des pr6cit£es publications n'a pu
trouver place le graphique repr£sentant le regime magn£tique de
Tile, il ine parait bon de faire figurer ici la petite carte, laquelle
servira, de la meilleure fa£on, a illustrer les considerations que j'ai
ailleurs developp£es.
Notre relevement magn£tique, comprenant la Sicile, Tunis,
Malte et les autres petites iles des mers siciliennes (tous ces points
d'observation, au nombre de 29, sont marques par un petit cercle
plein) a 6t€ achev£ entre le 10 juillet et le 17 septembre 1890. En
reportant done inalter£es sur la carte les valeurs obtenues, j'ai fait
le dessin valable pour Tepoque 1890.6, qui est sensiblement com-
mune a toutes les mesures.
Cependant, afin qu'on put tracer avec surety les courbes magnd-
tiques a travers les mers Ionienne et Africaine jusqu'aux limites
de la carte, j'ai fait aussi entrer en ligne de compte quelques deter-
minations effectu£es dans la pdninsule calabraise, par M. Chistoni
ou par inoi, en des £poques proches du 1890. Et, en ce qui con-
cerne le littoral oriental de la Tunisie, outre Tunis compris par moi
dans litineraire du 1890, j'ai choisi encore quelques stations parmi
celles que M. Moureaux et une mission hydrographique fran£aise
87
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88 £• PALAZZO [vol. iv. No. 2.]
avaient faites, peu d'anndes auparavant. Ces autres points sont
not£s par un petit cercle vide ; et pour raraener les respectives me-
sures k la m£me dpoque 1890.6, des determinations principales, j'ai
appliqu£ les valeurs des variations annuelles : — 5'.6 pour la d£cli-
naison, — i'-4 pour l'inclinaison, +0.00017 pour l'intensit£ hori-
zontale, le signe — indiquant diminution dans le temps. Ce sont
les coefficients de variation les plus probables, qu'on d£duit pour la
region sicilienne, autour de T6poque de nos observations*
Mais il ne faut pas croire que tous les points d'observation,
compris ainsi dans le cadre, puissent donner une bonne contribution
au trac£ des lignes isomagnetiques. En effet, on sait bien qu'au
dessous d'un sol volcanique, non seulement le champ magn£tique
terrestre est plus ou moins fortement trouble, mais en general les
valeurs des perturbations se montrent variables d'un point k
l'autre tr£s rapidement, avec des sauts brusques, m£me pour des
petites distances et souvent pour peu de metres, de sorte que les
valeurs des £l£ments magnetiques, dans leur succession, semblent
6chapper k une loi quelconque. Ce sont le sol volcanique au dessous
des boussoles d'observation et les roches £ruptives imm£diatement
voisines qui, £tant douses de susceptibility magn£tique et possedant
quelquefois des v£ritables pdles comme des aimants, produisent de
pareilles variations tres irregulieres. Ces faits, d'ailleurs jadis bien
connus, furent confirm£s aussi dans la campagne magu£tique de la
Sicile; ils ressortirent bien des observations que je fis sur les
petites iles volcaniques de Pantelleria, Ustica et Linosa. A cause
du manque de continuity dans les valeurs, il n'est pas raisonnable de
tracer les lignes isomagnetiques sur la base de determinations faites
dans des points sporadiquement diss6min£s sur un sol volcanique;
en d'autres mots, alors qu'il s'agit de territoires volcaniques, on ne
peut concevoir, sur une carte geographique d'6chelle ordinaire,
aucun systeme de lignes isomagnetiques, qui r6ponde k la realit£
des faits.
J'ai voulu bien faire ressortir la position et l'extension des re-
gions volcaniques, en couvrant par de fines hachures les respec-
tives portions sur le papier; c'est pour signifier que \k ou, sur mon
dessin, on voit les courbes isomagnetiques traverser des terrains
volcaniques, elles y perdent tout k fait leur signification: dans
ces endroits on considerera done les lignes comme interrompues.
L/allure des lignes tracees par moi est uniquement d6termin£e par
les valeurs obtenues dans les stations placees au dehors des terrains
volcaniques, bien que quelques-unes parmi elles offrent des ano-
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CARTE MAGNETIQUE DE LA SICILE
89
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90
L. PALAZZO Ivol. iv, No. 2.)
malies qui sont dues tr£s vraisemblablement a l'influence de masses
volcaniques agissant a distance. Pour expliquer mieux mon idee,
voici un exemple : Fisogone 9 30' qui court avec des sinuosit6s
le long de la c6te orientale de Tile, a 6t6 tracde de cette fa£on,
pas en s'appuyant sur les valeurs, irr£guli£res d'une mani&re dis-
continue, trouv£es en diff<6rents points de T^Btna, jusqu'au som-
met, mais en tenant compte seulement des resultats de Patti,
Taormine, Bicocca, Syracuse, Caltagirone, etc. Toutes ces stations
sont en effet au dehors du sol volcanique; plusieurs entre elles sont
pourtant sujettes a Taction a distance de massifs volcaniques, et
c'est pourquoi elles revelent des anomalies. Ces dernieres anoma-
lies gardent toutefois un caractere divers des autres mentionu6es
ci-dessus, c'est-a-dire elles paraissent ob£ir a uue certaine loi de
continuity. De m£me, la forte inflexion que subit l'isodyna-
mique 0.252 vers le sud jusqu'a toucher Taormine, est provoquee
par la valeur anomale trouv£e a Taormine m£me, qui est d£ja
hors de la region ^Etnee, et £loign£e de presque 7 km. de la limite
des coulees laviques du volcan.
D'apres ces criteriums la carte a 6t6 dress^e, et conform6ment
aux susdites reserves elle doit etre interpr£t6e.
Je n'insisterai pas maintenant a 6num£rer ici les diverses moda-
lit£s de chaque courbe en particulier, puisque je l'ai d£ja fait dans
ma Note presentee a TAcad^mie des Lynx£es. Un coup d'oeil sur
la carte suffit pour embrasser tout ce qu'il y a d'int£ressant dans la
disposition des lignes. On remarquera que, tandis que dans la plu-
part de l'ile et sur la mer Africaine n'existent presque pas des pertur-
bations sensibles, au contraire des anomalies bien saillantes ressor-
tent le long du littoral oriental. Et en effet, on rencontre ici d'abord
Timposantcdne volcanique de 1'iEtna, puis les formations basaltiques
assez 6tendues du Syracusain, et enfin, vers Textrdmit^ sud, le ba-
salte de Pachino; tout cela explique les remarquables contorsions
des lignes magn£tiques. J'ai et6 amen6 aussi a plier fortement vers
la terreferme Tisogone 9°o' et l'isocline 52°o\ a la suite des valeurs
anomales fournies par la station de Cozzo Spadaro, qui repose sur
un banc de calcaire hippuritique et subit cependant l'influence du
proche basalte de Pachino.
Mais il faut tout de suite noter que, comme la distance des
lignes d'egale d£clinaison et de celles d'£gale inclinaison a 6t6 choisie
de 30' seulement, ainsi les deformations des lignes isomagn£tiques
produites par le voisinage de terrains volcaniques paraissent tres
accentu£es dans la representation graphique sur la carte, quoique
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CARTE MAGN&TIQUE DE LA SICILE 91
en les consid£rant k leur valeur absolue, les anomalies ne soient que
peu de chose. En r£alit£, si nous prenons k examiner, par exemple,
les points anomals determinant les plissements plus profonds de
Tisogone 9 30', et nous comparons les valeurs y observes avec
celles qu'on aurait obtenues dans l'hypoth&se que la dite isogone
courtit sur le territoire sicilien tout en gardant une allure normale,
nous trouvons que rirr6gularit£ dans la d£clinaison serait de presque
8' en plus k Taormine et Bicocca, et de 15' environ k Syracuse
et Caltagirone, en plus et en moins respectivement pour ces deux
lieux. Analoguement, la station de Cozzo Spadaro serait anomale
seulement par des hearts d'un demi degr£ k peu pr£s, soit dans la
d£clinaison, soit dans l'inclinaison.
Quoique les anomalies des courbes magn£tiques autour de la re-
gion J£tn€e t d£cel6es k Toccasion du retevement magn£tique de la
Sicile, rentrent dans la cat£gorie des faits jadis connus sur Taction
magnetique des roches ign£es, et bien qu'elles (comme nous venons
de le faire observer) ne soient pas tr&s fortes en valeur absolue,
elles ne cessent pas, malgrd cela, d'etre assez intdressantes. Aussi, la
question du regime magndtique autour de T^Etna a paru m^riter une
£tude plus d£taill£e et complete, de 1'avis du M. Tacchini le savant
Directeur du Bureau Central de M£t£orologie. J'ai done repris,
dans Thiver pass6 (1897-98), Investigation magnetique tout k fait
sp^ciale aux alentours de l\<Etna, en m£nie temps que M. le pro-
fesseur Ricc6 de Catane s'occupait k determiner, avec le pendule de
Sterneck, les variations de la pesanteur sur le volcan. J'ai ex6cut6
les mesures, pas sur les champs de lave m&mes (ce qui, pour
les raisons exposes plus haut, n'aurait abouti a rien de concluant),
mais au contraire sur le terrain neutre tout autour des laves, k des
distances relativement petites, e'est-^-dire de 1 k 2 kilometres.
J'ai aussi multiple beaucoup le nombre des stations d'observation ;
celles-ci sont tr£s rapprochdes Tune de 1'autre, de 5 k 6 km. de
distance.
J'espfere de pouvoir sous peu communiquer aux lecteurs du
'Terrestrial Magnetism'* les r£sultats d£taill£es de cette rdcente
6tude. En attendant, je me bornerai ici k rapporter que les nou-
velles recherches dans les environs de TiEtna ont r£v£l£ des ano-
malies qui ob£issent assez bien k une loi de continuity, puisqu'elles,
dans de points ext£rieurs k la limite des laves, ne sont pas dues k
Tinfluence immediate des parties de roche volcanique les plus voi-
sines aux appareils de mesure, mais elles sont provoqu£es par une
sorte d'action d'ensemble des masses du volcan. J'ajouterai en outre
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92 L. PALAZZO [Vol. IV, No. 2.]
que j'ai trouv6 pour ces perturbations un ordre de grandeur interieur a
celui auquel je m'attendais; elles sont a peu pres du m^me ordre que
celles d£ja constatees pendant la campagne de 1890. A ce propos,
il n'est pas inutile de rappeler que dans le Gouvernement de
Koursk en Russie, dans une region ou les couches superficielles
sont notoirement d£nuees de tout £l£ment rocheux magn£tique, M.
Moureaux vient de d^couvrir des perturbations d'un ordre bien
sup^rieur a celles que nous avons mises en evidence dans le district
JEtn6. On apprend ainsi, peut-£tre avec surprise, que des roches
cachdes dans les profondeurs du globe peuvent parfois donner
origine a des anomalies beaucoup plus fortes que des roches a la
surface du sol manifestement magn&iques, telles que les laves de
1'iEtna.
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THE MAGNETIC WORK OF THE UNITED STATES ^
COAST AND GEODETIC SURVEY. 1
By L. A. Bauer, Chief of Division ok Terrestrial Magnetism.
PAST WORK.
In the " Plan for the Reorganization of the Survey of the Coast,
as adopted by a Board convened on the 30th of March, 1843, by di-
rection of the President of the United States," explicit provision
is made for the making of " all such magnetic observations as cir-
cumstances and the state of the annual appropriations may allow."
Since then Congress, by more or less generous appropriations, has
distinctly iecognized the importance of this feature of the work of
the Survey.
Under the first Superintendent, Professor F. R. Hassler, the mag-
netic declination (" variation ") was supplied, on the Coast Survey
Charts, as determined with the aid of the ordinary nautical instru-
mental means then in vogue. In the Transactions of the American
Philosophical Society, Philadelphia, 1825, Professor Hassler pro-
posed to measure relative magnetic intensity by means of oscilla-
tions of a needle, no method for absolute measurement being then
known.
The real magnetic work of the Survey, however, may be said to
have commenced with Professor Hassler's successor, Professor Alex-
ander Dallas Bache. Professor Bache had previously made a mag-
netic survey of Pennsylvania, which was not followed until in quite
recent years by the magnetic surveys of Missouri, New Jersey, and
Maryland. He had likewise established the first magnetic observ-
atory in this country — that at Girard College, Philadelphia — and,
while on a trip abroad, had made a series of magnetic observations
at various places.
Improved magnetic instruments were now imported, and the
expert aid of Dr. John Locke, of Cincinnati, and Professor Ren-
wick, of Columbia College, was temporarily employed. The three
magnetic elements — declination, dip, and intensity — were deter-
mined at various places, chiefly along the seacoast.
The work of magnetic observation, thus fairly started, has since
1 Published by permission of the Superintendent of the Coast and Geodetic Sur-
vey, Professor Henry S. Pritchett.
93
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94 L.A.BAUER [Vol. IV, No. 2.]
been prosecuted without interruption over the entire country and
Alaska by various Assistants of the Survey.
The following notes are taken almost verbatim from Mr. Schott's
various reports.
Isogonic Charts Published by the Survey.
The first table of declination results accompanied by an isogonic
chart * was published by A. D. Bache, Superintendent, and J. E.
Hilgard, Assistant, in the Annual Report for 1855, Appendix No. 47,
and plate No. 56. The declinations were reduced to a common
epoch — viz., 1850 — by means of assumed values of the annual
change, and for convenience of discussion the declinatious were ar-
ranged in geographical groups, which could be separately treated
by application of Lloyd's interpolation formula. The table com-
prises one hundred and fifty-three stations, and the isogonic curves,
computed for each degree of declination, cover but a narrow strip
along the coast-line. In the following year the same authors pro-
duced a new chart, as the result of a more extended discussion, in-
clusive of all recent observations, but retained the epoch 1850.
(See Annual Report of 1856, Appendix No. 28.) On plate No. 61
of the Report, the isogonic curves fairly cover the area of the east-
ern part of the United States, as well as the area bordering on the
Pacific Coast, and a connection is shown over the Gulf of Mexico
and along the Mexican boundary.
The Annual Report for 1861, Appendices No. 23 and No. 24,
contains two small isogonic charts (plate No. 30), designed for a
special purpose, and in aid of navigation along the southern coast;
epoch i860.
The Annual Report for 1862, Appendix No. 19, gives an ac-
count of a magnetic survey of the State of Pennsylvania, and on
plate No. 47 shows iso-magnetic lines laid down for the two epochs
1842 and 1862.
The next isogonic chart, constructed by Assistant C. A. Schott,
accompanies Appendix No. 19 of the Annual Report for 1865, plate
No. 27. It is on a larger scale, but covers about the same area as
the chart of 1856. It embodies, however, the results accumulated,
and uses the latest information respecting the secular change. The
epoch is 1870.
1 The first detail chart extending some distance into the interior of the country
was constructed by Professor E. Loomis for the epoch 1840, and published in Silli-
man's Journal Science and Arts, Vol. XL.
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MAGNETIC WORK OF COAST SURVEY 95
The next chart issued, Report for 1876, Appendix No. 21, plate
No. 24, is due to Assistant J. E. Hilgard. It is referred to the epoch
1875, afl d includes the results of the Survey up to 1877, and in part
to 1879, as well as about two hundred observations made from 1871
to 1876, under the auspices of the National Academy of Sciences
and at the expense of the Bache Fund. In this chart the isogonic
curves cover the whole of the United States, excepting Alaska, and
distinct notice is taken of certain large irregularities in the distri-
bution of magnetism which made themselves manifest in certain
regions in the eastern and central parts of the country. The
curves over the western part remain smooth and regular, the ob-
servations here not yet being sufficiently numerous for the safe de-
lineation of irregularities.
"Distribution of the Magnetic Declination for 1885." This
publication, brought out in the Annual Report for 1885, Appendix
No. 13, by Assistant C. A. Schott, is designated by him as the " first
edition/' on account of its completeness, a special chart for Alaska
and adjacent regions being included. The arrangement of the
table of results is alphabetic by States, with two subdivisions in
each, one for Coast and Geodetic Survey results, the other contain-
ing the results from all remaining available sources, as compiled
by the author; the table contains in all 2,359 stations. The re-
sults were reduced to the epoch 1885, with the aid of Mr. Schott's
extensive secular variation discussions. The curves for the United
States were determined by the graphical process, and were pub-
lished on a chart of scale — o™^, -, while those for Alaska and adja-
cent w T aters, on account of the scarcity of data, were made to de-
pend upon an interpolation formula established by the application
of the method of least squares ; these last curves were published on
a chart, to the scale of 77-^—. As far as the accumulated material
would permit, special notice was taken of all locally disturbed re-
gions, and the extent and the amount of the local deflections were
shown on the chart.
" Distribution 1 of the Magnetic Declination for 1890." This is
Mr. Schott's "second edition," and is contained in the Report for
1889, Appendix 11. The table of declinations comprises 3,237 sta-
tions; in all cases where a station has been repeatedly occupied,
only that observation nearest to the epoch 1890 is given. The
curves for the United States are again obtained by the graphical
method, and those for Alaska by a newly established interpolation
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gS L. A. BAUER [Vol. IV, No 2.)
formula. The writer had the privilege of assisting Mr. Schott in
the construction of these charts.
" Distribution of the Magnetic Declination for 1900." (Third
Edition.) The charts for the epoch 1900 are based on 3,591 tabu-
lated declinations. They are a great improvement upon the former
charts, the reductions to the epoch 1900 being based on a new and
very exhaustive discussion of the secular variation of the magnetic
declination at 118 stations, embracing 1,435 annual observations.
The steady improvement in the isogonic charts is made readily
apparent by a comparison of the earlier ones with those of recent
date. In the latter the curves are no longer beautifully curved
lines, but exhibit many sinuosities, showing that the magnetic
distribution, as it actually occurs in nature, is being more and more
truly represented. For Alaska, on account of the paucity of the
data, the distribution, as shown by the charts, must still be more
or less conventional.
ISOCLINIC AND ISODYNAMIC CHARTS.
The first complete discussion of the dip and the intensity ob-
servations was made by Mr. Schott for the epoch 1885. (See the
Annual Report for 1885, Appendix No. 6.) In the general collec-
tion of data, Mr. Schott makes an attempt to bring together, in sys-
tematic form, all observed dips and intensities within the bounda-
ries of the country, from the earliest to the present time. The
observations made at sea, being in general less accurate, are excluded
from the present collection, with the exception of a few results ob-
tained on the frozen sea ice off the coast of Alaska. The table
contains 1,999 results for dip and 1,523 for horizontal intensity;
only the most recent values, however, were used in the construc-
tion of the magnetic charts. In the table all intensities are ex-
pressed in absolute measure and in terms of the English units —
the foot, the grain, and the second of mean time. On the two ac-
companying maps, showing the distribution of the horizontal and
total intensities, the C. G. S. units are also introduced.
The discussion of the secular variation of the dip resulted in
the delineation, on the isoclinic map, of a belt of "no change" for
epoch 1885, with increasing dip on the one side, and decreasing dip
on the other. A similar feature was recognized in the discussion
of the secular variation of the horizontal intensity. We have also
pointed out to us the occurrence in about the year i860, for the
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MAGNETIC WORK OF COAST SURVEY
97
eastern part of the country, of a secondary maximum in the varia-
tion of the dip, as well as a minimum in the variation of the
horizontal component of the intensity. Upon the whole, the rep-
resentation of the dip for the epoch 1885 was far more satisfactory
than the representation of the horizontal intensity for the same
-epoch, the cause of this being ascribed to defective determination of
the instrumental constants in the intensity observations. This
-discussion has been in part superseded by the more recent one for
the epoch 1900.
The secular variation of the dip and intensity is now discussed
-conjointly with that of the declination. (See Report for 1895, Ap-
pendix 1.) For the 1 18 secular variation stations there are tabulated
and discussed 1,435 declination observations (annual values), 577 dip
results, and 479 horizontal intensity observations. The intensities
are all expressed in C. G. S. units. The curves described by the
north end of a freely suspended magnetic needle in the laspe of time
are drawn for a number of stations, and reversals in the more gener-
ally prevailing clockwise direction of motion are pointed out for cer-
tain stations along the Pacific Coast.
In Appendix 1, Report for 1897, tne distribution of the mag-
netic inclination and intensity is represented on three charts for
the epoch January 1, 1900, each to the scale of 7< J )0oo . The first
chart gives the lines of equal dip, the second those of equal hori-
zontal force, and the third the lines of equal total force. In the
table entitled " Collection of the Most Recent Magnetic Dips and
Intensities Observed in the United States and Referred to the Epoch
1 900.0/' results for dip and intensity are given for 164 1 stations, of
which 1,271. are within the United States; the stations are as yet
very irregularly distributed. These charts are decided improve-
ments upon the earlier ones.
Magnetic Observatories.
While the Girard College Observatory at Philadelphia, which
was in operation from 1840 to 1845, did not belong distinctly to
the Survey, it is not improper to include here a mention of it,
since Professor Bache continued to direct its work after he assumed
charge of the Survey. Mr. Schott, also, was later on employed in
the discussion of the observations.
The first Survey observatory was established under Professor
Bache at Key West, Florida, and was carried on from i860 to 1866.
The variations of the declination and of the horizontal and ver-
5
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98 L. A. BAUER [vol. iv, No. 2.1
tical intensities were recorded continuously by means of photog-
raphy, one of the Brooke magnetographs having been imported.
After a lapse of half a sun-spot cycle, the instrument was trans-
ported to Madison, Wisconsin, and put in operation from 1876 to
1880. The same instrument was then adapted for direct or eye
observations, and transported to Point Barrow, Alaska, where,
under the charge of Lieutenant Ray, magnetic records were ob-
tained for one year — 1882-83.
A superior self-recording magnetic apparatus, the Adie mag-
netograph, patterned after the Kew model, recorded the magnetic
variations, photographically, at Los Angeles, from 1882 to 1887.
This instrument was then set up at gan Antonio, Texas, in 1890,
and in September, 1892, it had to be removed, on account of elec-
tric-car disturbances, to Hillside Ranch, near San Antonio. The
observatory, unfortunately, had to be abandoned in March, 1895,
on account of the smallness of the appropriations for magnetic
work in that year.
The computations of the records from these observatories have
not as yet been completed, because of insufficient computing
force in the past. Only for Los Angeles has a complete discussion
been attempted.
Magnetic Work in the Polar Regions.
The magnetic records brought home by the Polar Expeditions
in command of Lieutenants Ray and Greely were placed in the care
of the Coast and Geodetic Survey. This material was subjected to
computation and discussion, and arranged for the press. The Point
Barrow work (1881-83) forms Part VI of the official publication
of Lieutenant's Ray's expedition (published in 1885), and the work
done at Fort Conger (1881-83), under Lieutenant, now General,
Greely, forms Appendix No. 139 of Vol. II of General Greely 's
official publication (1888).
PROPOSED WORK.
For many years, Mr. Schott has emphasized in his various re-
ports the pressing need of an expansion of the Survey work in
the line of terrestrial magnetism, if the Survey was to fulfill to
the best advantage all the purposes for which it was created.
He recognized, in the first place, that the magnetic work should
form a division of its own. Hitherto, all magnetic records have
been turned over to the Computing Division of the Survey, which,
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MAGNETIC WORK OF COAST SURVEY
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owing to the great variety of its work and the insufficiency of the
computing force, has been utterly unable to give the attention to
the magnetic work which the subject demanded.
That, notwithstanding these adverse circumstances, Mr. Schott
lias been able to accomplish so much in this special field, is due to
his untiring zeal and enthusiasm. In recognition of his contribu-
tions to terrestrial magnetism, the Paris Academy awarded him last
year the Wilde Prize of 4,000 francs. This honor, coming at the
time it did, was especially apropos, as Mr. Schott had just rounded
out a full half century of usefulness in the Survey.
It remained for the present Superintendent, Professor Henry S.
Pritchett, to perceive at once the need of expansion in magnetic
ivork. As a first step, a separate division has been formed, known
as the Division of Terrestrial Magnetism of the United States
Coast and Geodetic Survey. The chief of this division has full
•control of all magnetic work, both in the field and in the office.
The following preliminary outline will serve to give some indi-
cation of the character and scope of the work it is proposed to
•carry out with the enlarged opportunities.
1. Secular Variation Investigations.
The best evidence of the great demand for secular variation
4ata is the fact that, thus far, eight editions of Schott's secular varia-
tion paper have been successively issued by the Survey.
In all matters relating to the re-location of land boundaries, where
it is frequently necessary to know the precise amount of angular
•change in the direction of the magnetic meridian since the first or
original survey, the Coast and Geodetic Survey is recognized through-
out the country as the ultimate authority. The amount of money
^saved to landowners by such authoritative determinations as the
-Survey is able to furnish, can scarcely be estimated. It certainly
-exceeds many times the total amount to be spent for magnetic
"work.
Every effort will be made in the future to multiply and verify
the secular variation data, and requests for information on the part
of surveyors will be encouraged in every possible manner, and true
meridian lines established for them.
2. Magnetic Survey op the Country.
This involves the determination of the magnetic elements, dec-
lination, dip, and intensity, at various points throughout the land.
£00380
ioo L. A. BAUER [vol. iv. No. a.*
Just how close the stations shall be to each other depends upon the
special purpose to be accomplished with the means at hand, and
the magnetic character of the regions involved.
A magnetic survey has peculiar difficulties to contend with ; for
the quantities to be experimentally determined are forever under-
going changes — some periodic, others not periodic. A magnetic
survey must, therefore, be made to refer to some particular moment
of time, and such means must be taken as to enable one to reduce-
all the measurements, not only to the selected epoch of the survey,
but also, as occasion may demand, to some other epoch in the near
past or in the near future. Means must also be taken for the
proper elimination of all such errors as are to be referred en-
tirely to the particular magnetic instrument used; i.e., instrumental
errors.
These requirements call for :
a. Elimination of all variations of short period or of brief duration,.
such as the diurnal variation, seasonal variation, disturbance varia-
tion, by means of the continuous observations at magnetic observa-
tories, suitably situated, and in sufficient number for the area cov-
ered by the magnetic survey. This will require, in addition to the
permanent magnetic observatories, of which mention is made in an-
other connection, the establishment at certain base stations of tem-
porary magnetic observatories, more or less completely equipped.
In many cases simply self-registering, or eye-reading declinometers
will suffice for the equipment of the temporary or secondary ob-
servatories.
b. Elimination of the secular variation. For this purpose a cer-
tain number of well-selected stations distributed over the area with
some degree of uniformity — so-called "secular variation" or "re-
peat stations'* — must be established, where observations shall be
made with special care and repeated at certain intervals of time.
Mr. Schott's list of " secular variation stations," embracing thus
far 118 stations, will serve as an excellent basis in the selection of
the "repeat stations." The number must, however, be greatly ex-
tended, especially in the western part of the country, as only
about one-sixth of the stations included in his list lie west of the
Mississippi.
Were we to select one " repeat station" to every 10,000 square
miles — /. e. y one station for a land area such as is included in the
State of Maryland, for example, or that of Vermont — we should re-
quire 300 "repeat stations" for the United States alone. Whether
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MAGNETIC WORK OF COAST SURVEY 101
this number will be sufficient, must be the subject of a special in-
vestigation. The number will probably have to be increased, as
provision must also be made against some unavoidable loss in the
number of the "repeat stations" originally established, on account
of the encroachments of civilization.
c. Elimination of instrumental errors. Various European investi-
gators have found that the instrumental errors are frequently
larger than the purely observational errors. In order, therefore,
to make possible the strict interrcomparison of all our magnetic
work, a " reduction correction to the selected Coast and Geodetic
Survey Magnetic Observatory Standard" will have to be determined
at proper intervals of time, for each survey instrument used. Pro-
vision will also have to be made for the comparison of the "Coast
and Geodetic Survey Standard " with those of other countries.
At how many stations will it be necessary to determine the magnetic
elements? The areas of the countries at present belonging to the
United States are, approximately, as follows :
United States, 3,025,600 square miles
Alaska • 577.39Q " "
Hawaiian Islands, 6,250 " "
Porto Rico, 3,530 " "
Total, 3.612,770 "
Hence we control an area equal "to that of entire Europe, or
about one-fifteenth of the entire land area of the globe. As magnetic
surveys have been especially prosecuted in Europe, it will be of
interest to note the density of distribution of the magnetic stations
in two recent, fruitful magnetic surveys ; viz., that of Great Britain,
where there was one station to every 139 square miles; and that
of Holland embracing one station to every 40 square miles.
Suppose we were to decide upon one station, on the average, to
every 100 square miles — an end that we must hope to attain some
day — then we would require the determination of the magnetic
elements at 30,000 stations within the United States. At the rate
of 400 stations a year, the magnetic survey, as detailed as this,
would require for its completion at least 75 years. It is not well,
however, to have a magnetic survey extend over such a long inter-
val of years. The errors incurred in reducing the observations to
a common epoch would greatly exceed the errors of observation.
It is evident, then, that we must either have a very large num-
• ber of observers and instruments at our disposal so as to com-
plete the survey within a short interval, say ten years at the most.
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102 L. A. BAUER [vol. 1v.K0.2j
or we must content ourselves for the present with making a less
•detailed survey.
Let us say that our present means will enable us to com-
plete 450 stations per annum, of which 400 are to lie within
the United States. Suppose that at the end of the year 19 10 we
^hall have occupied 4,000 stations in the United States and have
made the necessary "repeat observations," and that the stations
liave been to some degree uniformly distributed, then we shall
liave on the average one new station to every 756 square miles.
Selecting as the epoch to which the observations shall be reduced
January 1, 1905, we would then have, with the addition of about
1,000 former stations, which we could utilize, a magnetic survey, the
stations of which would be distributed at the average rate of one
to every 600 square miles, or, approximately, one station to an area
35 miles, 40 kilometers, square.
This will give a very satisfactory representation of the distri-
bution of the earth's magnetism within our confines, and will suf-
fice for the accomplishment of many of the practical purposes of
magnetic surveys.
We will call this our " first survey," and, as stated, its epoch
"will be 1905. We shall now be able to tell in what portion of the
•country more stations are needed. That is, the density of the ul-
timate distribution of stations will not be a uniform one. In re-
gions where the distribution of magnetism is fairly regular, com-
paratively few stations will suffice, while in magnetically disturbed
areas the number of stations must be increased in conformity with
the character and extent of the disturbance. The subsequent
-work will consist then in filling in stations where most needed,
and repeating observations at the " repeat stations."
In short, the plan of conducting a magnetic survey of this
country, which appears to be best suited to the present conditions,
and one that it is possible to carry out within a reasonably short
time, is as follows: To make first a general magnetic survey of
the country with stations about twenty-five to thirty miles apart;
then, as opportunities present themselves, to add stations in the
magnetically disturbed areas. The observations at the "repeat sta-
tions," made from time to time, will furnish the proper secular va-
riation corrections.
The great advantages of this plan over that of attempting a greatly
^detailed magnetic survey at once, the steady progress of which
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MAGNETIC WORK OF COAST SURVEY
*°5
over the entire country, on account of its extent, would necessarily
be very slow, will be readily perceived. It will be of interest, how-
ever, to point out that the plan, as briefly outlined, will make it
possible, within a reasonable time, to construct two sets of magnetic
maps for the same epoch, each set based upon a different distribu-
tion of the stations. An opportunity will thus be afforded, as in
the case of the recent Magnetic Survey of Great Britain, to obtain
some idea of the accuracy with which the isomagnetic lines can be
determined. The satisfactory solution of this question will serve
as a valuable guide in future magnetic work.
3. State Magnetic Surveys.
Various State geologists, incited by the example set by the State
Geologist of Maryland, Professor William Bullock Clark, either have
already made plans or are making plans for detailed magnetic sur-
veys of their respective States, in co-operation with the Coast and
Geodetic Survey.
4. Magnetic Survey of Ocean Areas.
Provisions for the determination of the magnetic elements at
sea are likewise being made. With the many vessels at the service
of the Coast and Geodetic Survey, exceptional facilities for this^
purpose will be afforded. In fact, one of the chief duties of the
Survey is the supplying of magnetic data to the mariner. From am
economic standpoint, this feature of magnetic work is the one
really of the greatest practical importance. In recognition of this
fact, the Survey vessels will hereafter take advantage of every op-
portunity to obtain the magnetic elements on sea and on shore.
5. Magnetic Observatories.
The rapid, successful, and economical execution of the plans as:
above briefly outlined, requires the establishment, at certain points,,
of magnetic observatories, where the countless variations in the
earth's magnetic force are continuously and automatically recorded,,
enabling thus the proper corrections to be applied to observations,
made at stations at any hour of the day.
The present plans contemplate the establishment of a magnetic-
observatory near Washington City — this will be the Central or
Standard Observatory; another in the northwestern part of the
United States; one in the Hawaiian Islands, and one in Alaska.
With the co-operation of the observatories at Toronto, Mexico^
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104 £• A - BAUER [Vol. iv, No.-^.J
and Havana, and with the aid of secondary or temporary obser-
vatories established as occasion may demand, the areas to be sur-
veyed will be fairly well covered.
It is very much to be hoped, however, that our universities and
colleges will seriously consider the establishment of magnetic ob-
servatories. Many an institution which utterly lacks the means of
making a reputation in astronomical work, could still afford to in-
augurate telling work in terrestrial magnetism.
The United States stands at the bottom of the list of civilized
countries possessing magnetic observatories. Almost every Euro-
pean power of note maintains, not only one, but several permanent
magnetic observatories. France has four already established, and
four additional ones in process of erection ; and progressive Japan,
with its small strip of territory, has six continuously operating mag-
netic observatories.
The recent International Magnetic Conference recommended
the establishment of a magnetic observatory at the Lick Observ-
atory. It is earnestly to be hoped that this suggestion will be car-
ried out. It is unfortunate that the San Antonio observatory in
Texas had to be abandoned. A permanent observatory should be
re-established in this locality.
The scheme of work for the Coast and Geodetic Survey observa-
tories will embrace, in addition to the regular magnetic work, ob-
servations in atmospheric electricity and of the electric currents within
the earth. Such observations can be carried on with practically no
additional cost, and yet add greatly to the value of the observatory
work. Arrangements will likewise be entered into with the Pots-
dam Magnetic Observatory for the making of strictly simultaneous
observations of a special character.
The plan of referring the initiation and prosecution of mag-
netic work in this country to such a well organized department
as the Coast and Geodetic Survey, whose work is recognized uni-
versally as of the highest order, will readily be seen to have
decided advantages. In the first place, the machinery for carrying
on the work is already to a great extent in existence. The ob-
server engaged in geodetic or astronomical work can frequently in-
clude to advantage magnetic observations, and thus can often be
saved the chief cost of magnetic work — the occupying of stations.
Again, the care and refinement with which the geodetic and astro-
nomical work of this bureau is carried out will ever be an incen-
tive to keep the magnetic work of the same high order.
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UBER EINIGE PROBLEME DES ERDMAGNETISMUS
UND DIE NOTHWENDIGKEIT EINER INTER-
NATIONALEN ORGANISATION.
Von M. Eschenhagen in Potsdam.
Der Vergleich der zu absoluten Messungen des Erdmagnetismus
dienenden Instrumente verschiedener Observatorien ist eine viel-
fach erhobeue und durchaus gerechtfertigte Forderung. Die Er-
fiillung derselbeu ist nothwendig, wenn man die magnetischen
Landesaufnahmen verschiedener Lander mit einander combiniren,
ja wenn man auch nur die Constanz der Werthe ein und desselben
Observatoriums mit geniigender Sicherheit verbiirgen will. Man kann
sich nun die allgemeine Auf gabe stelleu, die augcnblickliche?i Werthe
der erdmagnetischen Kraft an zwei oder mehreren Orten mit gross-
ter Pracision zu vcrgleichen, eine Aufgabe, welche besonderes In-
teresse hat, wenn man die Frage nach der Existenz verticaler, die
Erdrinde durchsetzender Strome aufwirft, oder auch schon wenn
man gelegentlich der magnetischen Landesaufnahme die auf den
Stationen erhaltenen Werthe auf die des Observatoriums bezw. auf
eine einheitliche Epoche reduciren will.
Wir wollen im nachstehenden eine Discussion der Mittel und
Wege zur Losung dieser Aufgabe versuchen, indem wir dieselbe so
allgemein als moglich zu fassen suchen.
Der augenblickliche Werth eines magnetischen Elementes an
einem bestimmten Ort ist offenbar von eiuer ganzen Reihe von
Gliedern abhangig, die grosstenteils veranderlich, theils periodisch,
theils nicht periodisch sind.
Das allgemeine Problem fordert nun, aus alien Stiicken den
coustanten Theil herauszufinden, den wir den normalen nennen
konnen und dessen Potential eigentlich nur eine Function der
geographischen Breite sein sollte, wenn wir mit W. v. Bezold 1 die
Voraussetzung zu Grunde legen, dass die Erde in normalem Zu-
stande wie eine homogene Stahlkugel symmetrisch urn die Rota-
tionsaxe magnetisirt ist, eine Annahme die zwar eigentlich nur eine
Definitionssache ist, die aber dadurch gestiitzt wird, dass in der
Entwickelung des magnetischen Potentials der Erde gerade das
1 W. v. Bezold : Der normale Erdmagnetismus, Siizungsbcrichte der Berliner
Acad. 50. 1895.
6 105
sJ
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lo6 M. ESCHENHAGEN [Vol. iv, No. 2 ]
erste Glied, welches jene Abhangigkeit vom Sinus der Breite zeigt,
das Hauptglied ist, was bei dem Potential einer homogenen magne-
tischen Stahlkugel zutrifft. Es lasst sich zur Zeit allerdings nichts
dariiber sagen, ob jener normale Theil wirklich constant ist, die
Losung dieser Frage wird erst erreicht, wenn jenes erste Glied mit
wesentlich grosserer Scharfe als bisher von Zeit zu Zeit empirisch
dargestellt werden kann. Dies Ziel ist seit den Zeiten von Gauss
4ind Ermann verschiedentlich erstrebt worden. 1
Alle bisherigen Versuche konnen aber aus Mangel an sicheren,
uber die ganze Erde vertheilten Beobachtungen nicht die Precision
besitzen, mit welcher z. B. heute die Geodasie die Probleme der Erd-
messung und der Breiten variation, sowie der Vertheilung der
• Schwerkraft behandelt. Denn es befindet sich bei diesen Fragen,
die eine gewisse Verwandtschaft mit unserem Problem nicht ent-
behren, die Geodasie in einer wesentlich giinstigeren Lage, da bei
ihren Aufgaben die zeitlichen Veranderungen keine so bedeutende
Jlolle spielen.
Doch muss der Fortschritt, welchen diese Wissenschaft durch
<^onstatirung der Polhohenschwankung sowie durch Nachweis
^zahlreicher Anomalien der Schwerkraft erreicht hat, ein Antrieb
^sein, auch in der erdmagnetischen Wissenschaft die analogen Er-
^cheinungen scharfer zu verfolgen, da ein Zusammenhang ja nicht
:ganz ausgeschlossen ist. Wenn man erwagt, dass die Erde als ein
xotirender Magnet betrachtet werden kann, dessen magnetische
Axe nicht mit der Rotatiousaxe zusammenfallt, so kann dies
zur Folge haben, dass durch Einfliisse eines ausseren magnetischen
Kraftfeldes Verlagerungen der beiden Axen zu einander eintre-
ten, so dass eine Controle der Lage der magnetischen Axe sicher
von hohem luteresse sein diirfte.
Eine Analogie zu den zufalligen sowie den regelmassigen tag-
lichen und jahriichen Sch wan kungen kennt die geodatische For-
•schung entweder nicht, oder braucht sie bislang nicht zu beriick-
sichtigen, obgleich z. B. theoretisch ein Einfluss der Gestirne auf
•die Erdrinde, also korperliche Gezeiten wohl denkbar sind. Ande-
rerseits ist aber ein Zusammenhang der Anomalien der Schwerkraft
mit denen des Erdmagnetismus in dem Falle nicht von der Hand
zu weisen, wo sch were Eisenmassen in der Erde die gemeinschaft-
liche Ursache beider sein konnen.
1 Vergl. Neumayer's Atlas des Erdmagnetismus in Berghaus Physik. At/as und
-Ad. Schmidt : Neue Berechnung des erdmagnetischen Potentials, Abhandlungen.
*ier K. barer. Acad. d. H'iss. 1895.
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PROBLEME DES ERDMAGNETISMUS . j 07
Durch die Moglichkeit der Elimination jener periodischen und
nichtperiodischen Veranderungen des Erdmagnetismus wird der
Grad der Precision bestimmt, mit denen jenes oben erwahnte Prob-
lera der Darstellung, des normalen Erdmagnetismus, losbar ist, da.
eine zu rigorose Anforderung die Arbeit nur compliciren wiirde^
Es kommt also im wesentlichen auf die Frage hinaus, die wir im
Eingang aufstellten, namlich: it ie genau kann man die Wert he des-
Erdmagnetismus an zwei oder mehr verschiedenen Or/en mit einan-
der vergleichen ? Dabei spielt der Vergleich der Instrumente nur
eine untergeordnete, gewissermassen vermittelnde Rolle, die nicht
Selbstzweck ist, und ihre Entstehung nur dem Umstande verdankt*
dass es uns noch nicht gelungen ist, bei den sogenannten absolnten
Messungen und zum Theil auch bei den Variationsbeobachtungen
wirklich correct auf die Grundeinheiten der Lange, Masse und Zeit
zuriickzugehen. Es ist, um dies gleich zu erwahnen, unsres Er-
achtens fur ein gut ausgeriistetes magnetisches Observatorium ersteni
Ranges als unbedingte Forderung hinzustellen, dass die erdmag-
netischen Bestimmungsstiicke, sowohl fiir absolute als Variations-
messungen, an zwei Instrumentenserien ermittelt werden, die von
verschiedener Construction sind und so weit als moglich auf ver-
schiedenen Principien beruhen.
Dies ist wenigstens die zur Zeit einzige sichere Controle iiber
den Grad der Zuverlassigkeit der Messungen.
Die Vergleiche von mehreren so # lchen Observatorien schaffei*
dann die Moglichkeit, die iibrigbleibenden Inst rumen talfehler bis.
zu einem gewissen Grade unschadlich zu machen.
Es ist also das Bestreben, mit den besten instrumentellen Hilfs-
mitteln die grosste Genauigkeit in der Angabe der augenblicklichem
Werthe des Erdmagnetismus zu erreichen, in erster Linie fur eine
zielbewusste Forschung nothwendig, wahrend der Vergleich der
Observatorien die zweite Bedingung ist. Doch soil damit nicht in
Abrede gestellt werden, dass auch gelegentliche Beobachtungen
ihren Nutzen haben konnen, insbesondere dann, wenn sie im An-
schluss an ein Observatorium geschehen.
So hat z. B. eine einzelne Messung, die ein Gelehrter auf fr-
gend einem Platze der Erde ausfuhrt, nur einen untergeordnetei*
Werth, wenn er nicht mit seinem Instrument die Beobachtung an
einem Observatorium wiederholt und damit die Differenz seiner
Station gegen das Observatorium fiir eine gewisse Zeitepoche fest-
stellt. Um dies mit aller Scharfe zu erzielen, gehoren freilich eine
ganze Keihe von Controlmassregeln.
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io8 M. ESCHENHAGEN [Vol iv.sca.j
Der augenblickliche Werth M eines magnetischen Elements
hangt ab, erstens von dem sogenannten constanten oder normalen
Theile des Erdmagnetismus Mm, ferner von der magnetischen Ano-
malie des Ortes Af*> von der wir keineswegs wissen, ob sie con-
stant bleibt. Dieselbe hangt zum Theil von einer Querniagnetisi-
rung der Erde — parallel zur Aequatorebene ab, weiterhin aber
treten auch rein locale Anomalien auf, die mit dem Gebirgsmagne-
tismus wechseln. Alle Grossen konnen auch von der Temperatur ab-
hangig sein. Endlich kann als weitere Grosse, von denen M wahr-
scheinlich abhangt, die Meereshohe in Frage kommen, die wir zu
A/* hinzurechnen konnen. Diese Stiicke diirften den Theil aus-
machen, iiber dessen Veranderlichkeit nichts sicheres bekannt ist.
Nun kommen hinzu die periodischen Aenderungen, namlich die
tagliche, jahrliche und Sacularvariation, deren Amplituden be-
kanntlich nach Zeit und Ort variabel sind, endlich die anscheinend
zufalligen magnetischen Storungen, deren Amplituden ebenfalls
wechseln. Schliesslich fiigen wir noch eine Grosse hinzu, welche
den Instrumentalfehler bezeichnen soil, A/. Driicken wir jene
einzelnen Glieder als Functionen gewisser Veranderlicherer aus,
wobei wir h — hora, die Tagesstunde, h — dies, den Jahrestag und
/ — tempus, die seit der Epoche, mit der wir zu zahlen beginnen,
verflossene Zeit und endlich mit £±s die Stoning bezeichnen wol-
len, so konnen wir setzen:
Af*= A/. + A/ a + /, (A) % + /, (8) + / 3 (/) + Aj + A/.
Die Function /,, /a,/ 3 , sowie A J konnen an den einzelnen Ob-
servatorien, wie oben gefordert, genau ermittelt werden, ebenso die
Instrumentalfehler. Wir kennen aber das Gesetz der Verbreitung
der Perioden und Storungen iiber die Erde nur unvollkommen
und angenahert; wir wissen z. B. nicht, 6b dieselben von der Ano-
malie oder der Meereshohe abhangen. Die Abhangigkeit von der
Zeit ist z. B. fur die tagliche Periode erwiesen, insofern als die elf-
jahrliche Periode der Sonnenthatigkeit eine Rolle spielt.
Sollen wir also die augenblicklichen Werthe zweier Orte ver-
gleichen, so ist dies mit geniigender Sicherheit nur dann moglich,
wenn diese Orte Observatorien sind, wo, wie erwahnt. die Func-
tionen /,, / 2l / 3 und A«y bekannt sind.
Die nachste Aufgabe ist dann, den Instrumentalfehler zu elimi-
niren, was, wie bekannt, durch Vergleich der Instrumente am ein-
fachsten mit Hiilfe eines transportablen Apparats erreicht wird,
wie dies bereits von verschiedenen Beobachtern geschehen ist.
Die weitere Arbeit kann nun nach verschiedenen Gesichtspunc-
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PROBLEME DES ERDMAGNETISMUS
109
ten gefordert werden. Handelt es sich im Endziel darum, die
Orosse M» + M m an beiden Orten zu vergleichen, so wird man die
iibrigen veranderlichen Stiicke eliminiren miissen. Man vergleicht
also am besten Zeiten, an denen A«*=o ist, d. h man wahlt ruhige
*Tage aus. Den Einfluss von /, kann man an beiden Observatorien
ziffermassig bestimmen, insofern eine Abhangigkeit von Lange
{Ortszeit) und Breite vorhanden ist (alte Methode der Reduction
auf das Tagesmittel). Es ist aber vorzuziehen, ihn zu eliminiren,
indem man Tagesmittel ruhiger Tage vergleicht, wobei sich noch
zeigen wird, ob etwa ein Einfluss der sog. Nachstorung vorhan-
<den ist.
Sind die Observatorien in nicht allzugrosser Entfernung gele-
£en, so dass die Jahreszeit keine verschiedene ist, so wird deren
JSinfluss f 2 von selbst wegfallen und ebenso der von / 3> wenn die
Zeiten des Vergleichs nahe aneinander liegen. Anderenfalls miis-
sen wir den ersteren Einfluss wiederum durch Bildung des Jahres-
mittels zu eliminiren suchen. Hiermit diirften wir zu der Frage
gelangen, wie iiberhaupt der Werth fiir eine bestimmte Epoche
abzuleiten ist. Offenbar nicht, indem man die 24 stiindlichen
Werthe von Decbr. 31., Mittags, bis Jan. 1., Mittags, zu einem
Mittel fur Jan. 1., Mitternacht, vereinigt, sondern am besten noch
<iurch Bildung des Mittels aller stiindlichen Werthe eines Jahres,
wobei der Einfluss nicht nur jener Periodeu, sondern auch der
^Storungen moglichst unschadlich gemacht wird, allerdings in der
Voraussetzung, dass dieselben sich gegenseitig aufheben.
Der Vergleich dieser Jahresmittel zweier Stationen wiirde
•dann in seinem Verlauf vermuthlich noch eine Abhangigkeit von
-der elrjahrigen Periode so wie von der Sacularvariation zeigen,
-durch deren Elimination man erst zu einem sicheren Werth fur
«eine bestitnmt zu definirende Epoche kommen wiirde.
Es ist klar, dass bei verhaltnissmassig nahe gelegenen Statio-
nen schon in kiirzeren Zeitraumen vergleichbare Epochenwerthe
-erhalten werden. Vorlaufig scheiut dies allerdings, wie ein Ver-
such, Werthe von Pola und Potsdam zu vergleichen, gezeigt hat,
noch an der Unsicherheit der Instrumentalcorrection zu scheitern.
Etwas anders gestaltet sich die Aufgabe, wenn man das Auf-
treten der Storungen an zwei Orten vergleichen will. Es ist klar,
<iass man unter Umstanden dann ausser den Instrumentalfehlern
auch alle periodischen Erscheinungen, die von Orts- und Jahres-
zeit abhangen, eliminiren muss, um zu einem Urtheil iiber den An-
theil der sich nach Weltzeit richtenden Storungen zu gelangen und
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IIO M. ESCHENHAGEN [Vol. iv, No. 2.1
zu entscheiden, welchera Kraftesystem dieselben zuzuschreiben
sind.
Von besonderem Interesse wird es dabei sein, zu untersuchen,
ob die veranderlichen Grossen, die periodischen wie unperiodischen,
durch locale Bedingungen modificirt werden konnen, ob z. B. die
tagliche Periode oder Amplitude einer Storung eine andere in local
gestortem Terrain oder in verschiedenen Meereshohen ist, oder ob-
eine Abhangigkeit von der Vertheilung von Land und Wasser vor-
handen ist.
Als letztes Resultat kann man dann ermitteln, in wie weit die
unter Af»+A/, enthaltenen Glieder wirklich constant bleiben, oder
ob Verschiebungen iiber die ganze Erde eintreten, und wie weit
die Magnetisirung der ganzen Erde constant bleibt. Man wird
hierzu selbstverstandlich nicht bei dem Vergleich der Compo-
nenten stehen bleiben, sondern wie schon eingangs angedeutet, zu
Ableitung des Potentials des sog. constanten Theils des Erdmag-
netistnus iibergehen, nachdem die veranderlichen Kraftsysteme,
die moglicherweise nicht einmal alle ein Potential besitzen, elitninirt
und — wie schon Gauss vorschlug — einer eigenen Betrachtung unter-
worfen worden sind.
Es sind also, wie wir gesehen haben, eine ganze Reihe von
Einzelaufgaben zu losen, ehe das Endziel erreicht werden kann.
Die Bearbeitung derselben hangt, wie schon oben betont wordea
ist, in erster Linie von einer exacten, zielbewussten Einzelarbeit in
den Observatorien, aber noch mehr von einem planmassigen Zu-
sammenarbeiten derselben ab. Es ware erwiinscht, wenn hiermit
in der Weise begonnen wiirde, dass sich zunachst mindestens drei
Observatorien vereinigen und dn gegenseitige Controle ihrer
Instrumeute und der Werthe der erdmagnetischen Elemente all-
jahrlich wiederholen. Der anerkennenswerthe Anfang, der hier-
mit von einzelnen Forschern, insbesondere durch van Rijckevorsel
gemacht ist, wird also nach der angedeuteten Richtung erganzt
werden mussen.
Als ein weiteres Ziel sollte man in's Auge fassen, ein inter-
nationales, gemeinschaftliches Observatorium einzurichten, das
alsdann als normal angenommen werden kann. Der Zeitpunct,
diesem Vorschlage naher zu treten, diirfte besonders fiir die Staa-
ten Europas nicht ungiinstig sein, da von deren verhaltnissmassig-
dicht gedrangt liegenden Observatorien voraussichtlich das eine
oder andere durch Einflusse electrischer Bahnen und Betriebe fur
feinere Untersuchungen insbesondere Erdstrombeobachtungeni
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PROBLEME DES ERDMAGNETISMUS 1 1 1
xmbrauchbar werden diirfte. Ein solches internationales Obser-
vatorium wiirde alsdann auf einer Insel ohne erhebliche Local-
^torung anzulegen sein, auf der es daher gegen alle Einfliisse der
Industrie u. s. w. fur immer gesichert ist. Man konnte hier z. B.
-an eine der kleineren englischen Inseln im Canal denken.
Die grosse Aufgabe verlangt aber die Errichtung einer ganzen
Anzahl solcher Observatorien an entsprechend gewahlten, iiber die
Erde gleichmassig vertheilten Orten. Hier bietet sich fur die
grosseren Staaten Gelegenheit im Fortschritt der wissenschaftlichen
Arbeit nicht hinter ihrer industriellen und Civilisations-Entwick-
lung zuriickzubleiben. Es ist daher mit Freude zu begriissen, dass
-die Vereinigten Staaten Nordamerikas, deren Einfluss sich iiber
mehr als die Halfte der Erdkugel erstreckt, und die sich fur lange
2eit mit dem einzigen Observatorium zu Washington begniigt
haben, jetzt im Begriffsind, ein zweites auf Honolulu zu errichten. 1
Bekanntlich genugen schon acht gut situirte Observatorien,
inn die wichtigsten Coefficienten des erdmagnetischen Potentials
b^stimmen zu konnen. Die Forderung ist demnach keine so
grosse, als dass sie — wenn freilich auch nur genahertden Anspriichen
der Theorie entsprechend — nicht erfiillbar ware, Es ist dabei zu
•erwagen, dass diese Institute auch anderen Wissenszweigen, insbe-
sondere der Geodasie von Nutzen sein konnen. Die Internationale
Erdmessung richtet zur Zeit vier Stationen auf dem 39 Breiten-
parallel (Nord) ein, sie geht hier mit eiuem Beispiel voran, welches
die erdmagnetische Forschung zur Nachahmung oder eventuell
zum direkten Anschluss anregen sollte.
Zunachst ist aber vor allem ein engerer Zusammenschluss der
hetheiligten Observatorien nothwendig, behufs Ausarbeitung eines
bestimmten Programmes. Die Schaffung einer solchen Organisation
musste die Hauptaufgabe der riac listen inter nationalen Confer en z sein.
Der Austausch von allgemeinen und besonderen Forschungsergeb-
nissen, wie derselbe auf der Versammlung der British-Association
zu Bristol 1898 stattfand, bietet gewiss eine Fiille von wissenschaft-
lichen Anregungen, indess sind die dort vom internationalen
Comitee gefassten Beschlusse schliesslich mehr oder minder nur Em-
pfehlungen der in ihnen niedergelegten Gedanken. Ein Fortschritt
in der in diesen Zeikn angedeuteten Richtung lasst sich nur erzie-
len durch Aufstellung eines gemeinsamen Arbeitsprogrammes, zu
dessen Inuehaltung alle zustimmenden Theile sich verpflichten.
1 It will appear elsewhere (p. 98), that the United States is making active prepa-
rations for the vigorous prosecution of a magnetic survey, and for the establishment
of several magnetic observatories.— Ed.
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H2 Af. ESCHENHAGEN [Vol. IV, No. a J
In zweiter Linie ist die Zusammenbringung von Geldmitteln
nothwendig, was in derselben Weise wie bei der internationalen
Erdmessung durch Staatszuschiisse geschehen muss, da nicht
anzunehmen ist, dass von Seiten Privater geniigende Mittel zur
Verfugung gestellt werden. Ein Anschluss an die Arbeiten der
Erdmessung diirfte, wofern sie iiberhaupt moglich ist, manchen
Vortheil bieten, er ist auch aus dem Grunde in Erwagung zu
ziehen, weil in vielen Landern nicht eine solche Arbeitstheilung in
der Wissenschaft eingetreten ist, wie es in manchen Staaten
Europas, speciell in Deutschland, der Fall ist.
Zunachst ware es wohl von Wichtigkeit, wenn das in St.
Petersburg in diesem Jahre zusammentretende internationale Me-
teorologische Comitee sich mit der Frage eines engeren Verbandes
der magnetischen Observatorien beschaftigen und eventuell die
Grundzuge fur ein systematisches Zusammenarbeiten aufstellen
wiirde.
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THE SECONDARY MAGNETIC FIELD OF THE EARTH. 1
By A. W. Rucker, Sec. R. S.
The magnetic field of the earth may be regarded as that pri-
marily due to a uniformly magnetized globe disturbed by some sec-
ondary causes. The probability that the primary field is produced
by a deep-seated system of electrical currents (whose genesis we
can not explain), is increased by the fact that iron, magnetite, and
basalt all become non-magnetic if the temperature be raised to the
neighborhood of a red heat. The same magnetic effects could be
produced on the surface either by magnetized matter or by electrical
currents properly distributed within the globe. But if the enor-
mous pressures to which the internal portions of the globe are sub-
jected do not affect the properties with which we are dealing, mag-
netizable matter can only exist very near to the surface. As we
penetrate from the surface downwards, the temperature rises by
about i° C. for every 90 feet, or (say) 37 per kilometer, and if this
rate of increase is maintained, the temperature at which iron be-
comes non-magnetic (which is different for different specimens)
would be reached at a depth of about 20 kilometers. Some experi-
ments made in my laboratory by Messrs. Barton and Williams in-
dicate that for magnetite the limiting temperature is less (about
557 ), and would be reached at a depth of about 15 kilometers. It
is convenient to call that stratum in the earth at which all matter
ceases to be magnetic, the magnetic floor,
Mr. Henry Wilde has imitated the primary field of the earth by
an arrangement of currents. Inside a globe eighteen inches in di-
ameter a smaller sphere was placed, and a wire was coiled round
this in planes inclined at an angle of 23 30' to the plane of the
equator. Between the two globes was a spherical shell of wire
gauze, round which another wire was coiled in planes perpendicular
to the geographical axis. Currents which could be separately reg-
ulated could be passed through the two circuits. The whole ar-
rangement was so adjusted that any part of the globe could be
brought under a support on which a small compass or dip-needle
could be placed at pleasure. The field due to the currents was
iThe following article is an expanded account of part of a lecture on " Earth
Currents and Electric Traction," delivered by Professor Rucker before the Royal In-
stitution, on April 14, 1899.
7 113
s)
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H4
A. W. Rl CKER [vol. iv. No. a ]
about ten times the earth's field at the point where the readings
were made. The axis of the inner sphere could be made to revolve
when inclined at a constant angle to that of the external globe,
and an attempt was made to imitate the secular change by this
revolution. This attempt was only partially successful, and, for
the moment, I propose to discuss only the particular arrangement
by which the existing state of the earth's surface was represented.
For any one position of the axis of the internal globe, the whole
of the interior arrangements above described are equivalent to a
uniform magnetization, parallel to an axis cutting the surface some-
where between the geographical pole and the arctic circle. Such an
arrangement, as we know, will not represent the magnetic state of
the earth; but after various trials, the history of which I need not
recount, Mr. Wilde hit upon the expedient of covering with thin
sheet-iron those portions of the interior surface of the outer globe
which correspond to the oceans.
The result has been described by himself as follows: "The de-
vious lines of the declination which had hitherto resisted all at-
tempts to reduce them to order, and masked the simplicity of the
primary phenomena of terrestrial magnetism set forth in the pre-
ceding propositions now presented themselves as secondary phe-
nomena — the effect of the unequal curvature of the terrestrial sur-
face during the secular refrigeration.
"The declination at the Cape of Good Hope, latitude 34 S.,
which was only 19 maximum without the iron covering, was now
30 W., the amount required for the epoch; while the declination at
Cape Farewell was now 42 ° W.
" The southern hemisphere of the globe also contained two lines
of no declination, nearly coincident with those on the charts for the
epoch 1880, and four lines of no declination similarly coincident in
the northern hemisphere ; two of which lines on the North Ameri-
can and European continents being continuations of those in the
southern hemisphere. But the most remarkable and unexpected
feature of the distribution of the magnetism on the iron covered
globe was the reproduction of the oval area of small westerly dec-
lination in Eastern Asia, between longitude no° E., and 160 E. ;
surrounded by large areas of eastern declination. The oval
also agreed in detail with that on the chart in having the largest
westerly declination, about 8° in the center, between the lines of no
declination.
11 Scarcely less interesting was the reproduction of the oval area
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EARTH'S SECONDARY MAGNETIC FIELD
"5
of small easterly declination about 5 , surrounded by a large area
of greater eastern declination in the equatorial parts of the Pacific
(i2o°-£7o° W.), while the unsym metrical form of the magnetic equa-
tor was very similar in its deviations to that of the terrestrial globe
for the epoch 1880." 1
Mr. Wilde has been kind enough to present one of his globes to
the National Collection of Scientific Apparatus at South Kensington.
His observations on the agonic lines and the magnetic equator have
been repeated, and their general accuracy confirmed by Mr. Forsyth
in the laboratories of the Royal College of Science.
The above is, I think, a fair account of Mr. Wilde's ' ' magnetarium ' '
as described by himself. In a later document he refers to the fact
that, in addition to the iron used in covering the seas, bands of sheet-
iron were placed on "the areas of the mapped globe occupied by
the southern mountain ranges of the Asiatic Continent. A similar
polarizing band was also required over the South American Conti-
nent to bring into adjustment the zero line with that of the chart
of the declination. " '
Mr. Wilde has recently informed me that some other polarizing
bands were also used, which apparently were not mentioned in his
accounts of his model. It is, therefore, a matter of interest to know
how far the close agreement shown in the above map between the
real and artificial agonic lines is due to the action of these bands.
On this point Mr. Wilde is unable to give me precise information, and
as I do not feel justified in dissecting a model deposited at South
Kensington, it will be desirable to investigate the matter anew.
Again, Mr. Wilde only shows the agreement between certain
principal lines (agonic, magnetic equator, Pacific oval) as
given on the. magnetic maps for 1880, and as deduced from
his model. Some preliminary experiments lead me to doubt
whether the agreement is satisfactory for the intermediate
isogonal lines. Thus the two isogonals of 20 westerly decli-
nation, which, in 1880, intersected in mid- Atlantic, appear to be
much distorted. It must therefore be clearly understood that I
think that both the nature of the results attained by Mr. Wilde
and the method of obtaining them require further investigation.
He has certainly succeeded in imitating the principal magnetic
lines by a combination of inducing and induced magnetization,
and he attributes his success primarily to the fact that he cov-
ered the oceans with thin sheets of iron. It is very desirable,
• Quoted from a description of Mr. Wilde'9 magnetarium, circulated by himself.
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n6 A. W. RUCKER ivol. iv. No. 2.}
before further experiments, which are likely to be tedious and
costly, are undertaken, to consider, on a priori grounds, whether
it is worth while to devote time and attention to a theory which
assumes that the earth beneath the oceans is more highly mag-
netizable than that beneath the continents. In connection with
this point it will be necessary to examine in greater detail the
conditions under which Mr. Wilde's experiments were performed.
Before investigating the matter further, I must admit that I feel
a certain repulsion in dealing with a question of so highly specu-
lative a nature, and I have no doubt that many of my readers will
be inclined to put aside the suggestion that the earth beneath the
seas is more magnetic than elsewhere as almost unworthy of dis-
cussion. On the other hand, it must be remembered that in the
past we have had hardly a glimpse of an explanation of the causes
of the phenomena of terrestrial magnetism, and that in approach-
ing so difficult a subject we must beware of not breaking the first
canon of scientific research, viz., that in studying a phenomenon
of which the causes are unknown, we must clear our minds of all
a priori theories, or at all events use them only as working hypoth-
eses. In spite, therefore, of the fact that we must deal with sug-
gestions which we can never hope to verify by direct experiments ;
that we must make assumptions as to the constitution of the earth
at depths we can not reach, — in spite of the essentially speculative
character of the whole inquiry, I think that, with Mr. Wilde's
model before us, it is our duty to ask whether there is anything
physically absurd and scientifically impossible in the hypotheses to
which the construction of that model points.
Apart, then, from the crude statement that from some unknown
cause magnetic matter has accumulated under the seas, is there
any reason for supposing that, if there is magnetizable matter
within the earth, there would probably be a thicker layer of it be-
neath the oceans than beneath the continents? To this we can at
once answer that unquestionably there is, and that it was indicated
by Mr. Wilde himself. The Challenger expedition proved that the
bottom of the deep ocean is at a temperature only a few degrees
above that of melting ice. The surface temperature, of course,
varies with the latitude ; but the bottom of the deep sea is every-
where very cold, and even in cases like that of the Mediterranean,
where the communication with the Arctic regions is practically
barred by the comparatively shallow straits of Gibraltar, the bot-
tom of the sea is at a temperature far below that attained at an equal
depth below the surface of the land.
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EARTH'S SECONDARY MAGNETIC FIELD
117
The average depth of the ocean is about 4 kilometers, and thus,
if we assume that we are dealing with rocks of uniform thermal
conductivity and that the bottom of the ocean and the surface of
the land are of the same temperature (a most unfavorable assump-
tion in the case of the tropics), the magnetic floor, or the isother-
mal surface corresponding to the temperature of no magnetization,
would be about 4 kilometers deeper within the surface of the globe
under an ocean of average depth than under a continent. Beneath
the deepest parts of the ocean the difference in the position of the
magnetic floor would be increased.
If, then, we suppose that at and for some distance below a depth
of 20 kilometers the earth is composed of matter which is mag-
netic below a certain temperature, and is of the same thermal con-
ductivity as rock, no part of this material would be magnetizable
under the continents, while under the oceans a layer of an average
thickness of 4 kilometers would be magnetized by the earth's field.
If the surface of the shell of magnetizable matter is at a less
depth than 20 kilometers, it would be magnetized everywhere ; but
the magnetized portion would, on the average, be 4 kilometers
thicker beneath the ocean than elsewhere.
If the surface of the shell is at a depth greater than 20 km.,
but less than that distance plus the greatest ocean depths — say less
than 28 km. — the average thickness of the magnetized portion be-
neath the sea would be less than 4 km.
It thus appears that if the earth is composed of magnetizable
materials, or if there is in the earth a thick shell of magnetizable
matter of which the depth of the upper surface does not exceed
20 km., and if the great pressures to which such materials would
be subjected do not completely modify their magnetic properties,
the thickness of the layer below the temperature of no magnetiza-
tion will be greater beneath the seas than elsewhere. Hence this
additional thickness may be the physical fact which Mr. Wilde has
represented by thin sheets of iron covering the ocean areas.
Since we have, then, not only a very remarkable agreement be-
tween the model and the magnetic state of the surface of the
earth, but also a vera causa which indicates that the model may be
an approximate representation of the true physical state of the
earth, it remains to discuss whether the disturbances of the earth's
magnetic field could really be produced by magnetic matter of
which the upper surface is at a depth not exceeding 20 km. and of
thickness comparable with 4 km.
For in several important points Mr. Wilde's model differs from
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1 18 A. W. RUCKER [vol. i\\ no. a.)
the true state of the earth, and in some respects ihe experiments
are imperfect. Thus, (i) the magnetic forces at different points
have not been compared ; (2) the central points of the compass and
dip-needle employed are not at the same distances from the surface
of the globe. If that surface is to be taken as corresponding to the
surface of the earth, the centers of the declination and dip-needle
were at distances from it which on the natural scale would corre-
spond to 700 and 1,400 km. respectively. Taking the mean of these
as about 1,000 kilometers, it is evident that the observations were
made at a distance at which the form of the magnetic field would
be appreciably different from that close to the surface of the globe.
In the model, relatively powerful forces would be produced close to
the edges of the iron plates, to which nothing on the surface of the
earth corresponds. These might be much reduced by supposing
the plates to thin out gradually, or to diminish in permeability, as
the edges are approached. But apart from a point of this kind, in
which the model could not be expected to imitate nature exactly,
the more prominent features of the earth's field would be modified
at a distance from the earth's surface of about one-sixth of its
radius to an extent which could be calculated from the Gaussian
expansion. Thus it was found to be important to cut a hole in the
iron coating roughly corresponding to the West Indian Islands.
The length of this is comparable with the distance of the center
of the declination needle from the earth's surface; the breadth
must be much less. It is evident that the effects of such a gap in
the magnetic field would be very different close to it and at a dis-
tance from it comparable with its largest dimension; and, further,
that the effects as measured by needles about 700 kilometers in
length would be very different from those actually recorded in a
magnetic survey.
All these arguments, therefore, tend to prove that if the mag-
netic matter represented by Mr. Wilde's iron sheets has a real ex-
istence, it must be at a depth of 1,000 kilometers below the surface of
the earth, and that in his experiments the radius of the earth must
be taken to be the mean distance of the centers of his exploring-
magnets from the center of the globe. Unless, therefore, these argu-
ments can be met, the hypothetical magnetic matter will be beneath
the magnetic floor, and its existence could only be accounted for
by an unwarranted assumption as to the effects of pressure on the
magnetic properties of bodies.
An attempt might be made to evade the difficulty by assuming
that the effects represented by the magnetization of the iron coat-
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EARTH'S SECONDARY MAGNETIC FIELD
119
ing are really due to systems of electric currents, but no good rea-
son can be assigned why these should closely simulate the presence
of a magnetic shield.
On the whole, then, we can not adopt a more favorable view
than that if it were shown to be possible to reproduce as good a
representation of the magnetic state of the earth's surface as Mr.
Wilde has made, when the exploring needles were close to the
iron coating, and when the gaps and edges were replaced by more
widespread and gradual changes of permeability, it might be pos-
sible to regard the experiment as having been performed under
conditions consistent with the view that the shielding material is
above the magnetic floor.
It is, however, worth while to assume that these difficulties are
overcome in order to inquire whether, even in that event, any in-
superable physical obstacle would be revealed. It might, for in-
stance, be capable of proof that the irregularities in the magnetic
field of the earth could only be produced by an iron shell much
thicker than the distance between the surface of the earth and the
magnetic floor. Such points must, therefore, be considered before
any further labor is expended on the investigation.
The thickness of the iron plates used by Mr. Wilde was 0012
inch = 048 mm., and as they were "tinned" the actual thickness
of the iron would be somewhat less than this. Now, as the radius
of the globe was 9 inches, 0012 inch = 5*2 miles or 8.4 kilome-
ters, which is greater than the average depth of the ocean, but
less than the depth of the magnetic floor below the bottom of the
ocean.
As far, therefore, as the plate used is concerned, no physical
impossibility is revealed ; but this argument proves very little, for
the material of the magnetic layer which the iron coating repre-
sents, the magnetic field in which it is placed, and its temperature,
would all be different from those of iron coating itself.
It may be useful, therefore, to consider the matter more fully.
Dr. Bauer has recently published a map of the residual field of
the earth, obtained when the forces due to a uniform magnetization
are subtracted from those which are actually observed on the sur-
face. If we assume that this residual field is due to Mr. Wilde's
magnetic layer, we may get some idea of what the thickness of that
layer must be for a given permeability. At the points where the
residual field is most powerful the forces amount to about d= 0*4 of
the calculated uniform field. This ratio is attained at a few
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120 A. W. RUCKER [vol. iv v no. 2.)
points only. The average ratio of the residual to the uniform field
would be about ± o*i or ± 02 of the latter.
Now, if we suppose the earth to be surrounded by a uniform
magnetic shell shielding the force produced by an internal uniformly
magnetized sphere, non-magnetic, it is evident that, by cutting holes
in the shell, or making parts of it non-magnetic, 1 we could impose
upon the primary field secondary disturbances, the ratio of which
to the unshielded field would depend upon the form of the holes
and the thickness and permeability of the shell.
The whole potential would consist of two parts, — that due to the
internal inducing sphere, and that due to the magnetism induced
in the fragments of the shell. If the latter part, when expanded
in spherical harmonics, contains a term corresponding to uniform
magnetization, then the corresponding term in the expansion of the
whole potential outside the shell will not give the potential due to
the uniform magnetization of the internal sphere, but that poten-
tial modified by the term due to the magnetization of the shell.
If, then, we suppose Dr. Bauer's argument to be applied to a
globe constituted as Mr. Wilde's model assumes, the primary mag-
netization, as calculated, may differ appreciably from that really
due to the internal sphere, and thus an appreciable error may
be introduced into the determination of the secondary field. Of
course Dr. Bauer was well aware of this fact, and his method is per-
fectly legitimate as an approximation ; but when we compare the
results with a physical theory, it is important to remember that the
true primary and secondary fields, defined with reference to induc-
ing and induced systems of magnetization, may differ considerably
from those defined with reference to the first and following terms of
a Gaussian expansion.
While on this point I may also remark that the interesting sug-
gestion made by Dr. Bauer, in the last number of ferrestrial Mag-
netism, on a possible connection between the secondary magnetic
field of the earth and the isabnormals of temperature, is open to
the objection that the deviation of the average temperature of any
points at the suriace of the ocean from the average for the corre-
sponding latitude is a surface phenomenon, which at points near
the bottom of the ocean is completely masked by the influx of cold
water.
» It is hardly necessary to point out that, though the magnetic effects of these
two arrangements would be identical, the one would and the other would not pro-
duce gravitational irregularities on the surface.
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EARTH'S SECOND AR Y MAGNETIC FIELD 1 2 1
His theory would therefore compel us to look for the source of
the secondary magnetic field at depths less than the ocean bottom.
Taking Dr. Bauer's numbers as they stand, I have determined
the ratio of the secondary or residual to the primary forces at a few
points, and, as has been stated, the results indicate that, on the
average, the resultant is about 1*2 of the primary force in regions
where the secondary force strengthens it, and about o*8 where the
two forces are opposed. These figures do not pretend to any great
accuracy, but are sufficiently near the truth for preliminary calcu-
lations.
Now, I take it that if we calculate the thickness of a uniform
shell of given permeability, which would reduce the intensity of
the true primary field in ratios similar to those given above, we
shall get an idea of the order of the magnitude of the thickness of
the broken shell necessary to produce the observed variations.
The method is very rough, and would be of very little use in ex-
treme cases; but it will serve to indicate whether there is any
physical impossibility in Mr. Wilde's assumptions. We will take
two ratios of the shielded to the unshielded field; viz., the ratio of
the smaller secondary to the primary field — /. <?., o*8 — and the ratio
of the smaller to the larger secondary field—/. *\, o*8/i*2=2/3*
The argument will be strengthened if somewhat similar results are
obtained when we substitute the maximum for the average sec-
ondary forces. In this case the two shielding ratios correspond-
ing to the above would be o'6 and 06 /r^.— 3/7.
If, then, / be the thickness of a shell of large permeability n %
and if a be the radius of the shell which is large compared with /,
the ratio of the shielded to the unshielded field, E, in the case
under consideration, is given by the formula :
3 + 2lfi/a
Hence, substituting the above values for E t we get the follow-
ing results:
TABLE I
a/3
e =3/5 I 3/7 i 4/5
t fi '
I
a
3/8
3/4
The second of these values of / n/a is almost certainly too
large. It is based upon the assumption that in order to produce,
8
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I2 2 A. W. RUCKER [Vol. IV, No. a.)
by means of a pierced shell, variations in the forces between a
certain maximum (Af) and minimum (m) value of the ratio of the
disturbed force at any place to the force at that place derived from
the first term in a Gaussian expansion, it is necessary to have a
shell which, if complete, would reduce the forces produced by an
internal uniformly magnetized sphere in the ratio Af/m. This is
manifestly exaggerated if we take edge effects into account, and
is, I think, too large, even if we omit regions very near to the
edges.
We next have to decide what value we may assume for the per-
meability. The three materials which we may regard as being,
with greater or less probability, at our disposal, are virgin iron,
magnetite, and basalt. The permeability of very magnetic speci-
mens of the last material is only of the order roi, and it may be
put aside as quite incompetent to produce the observed effects.
As far as I am aware, the most trustworthy measurement
hitherto made of the permeability of magnetite is an unpublished
experiment of Professor S. P. Thompson's, which he kindly allows
me to quote. Using the ring method, he found the permeability
in small fields to be about 4. Both Messrs. Barton & Williams
(loc. cit.) and I (Proc. Roy. Soc. 48, 1890, p. 592) have shown that
the permeability of magnetite rises with temperature ; but on the
basis of Professor Thompson's experiment, I do not think that we
can assume that it would rise as high as 10. On the other hand,
different specimens of a natural mineral, such as lodestone, may
differ enormously in permeability, 1 and it would be unsafe to base
any definite conclusions on a single experiment. All that can be
said is, that unless future observations should show that the per-
meability of large masses of natural magnetite is of the same order
as that of iron, it can not be the shielding substance.
Taking the largest of the ratios of the shielded to the unshielded
fields given in Table I, viz. 4/5, the thickness of shell of permeability
10 which would produce this reduction would be about 5 per cent
of the radius. Hence, in the case of the earth, the shell of mag-
netite would be at least 3 1 5 kilometers in thickness. As this is fifteen
times the depth of the magnetic floor, it is evident that Mr. Wilde's
iron shell can not represent a shell of magnetite, unless further in-
vestigation shows that the average permeability of that material is
1 Another experiment of Professor Thompson's, but not made by the ring method,
indicates that this may be the case.
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EARTH'S SECOND AR Y MAGNETIC FIELD 1 23
far above that of Prof. S. P. Thompson's specimen, or unless the
effects of great pressure neutralize those of temperature.
Considering next the case of iron itself, we know (1) that the
permeability of impure specimens may be very low, and (2) that
the permeability at ordinary temperatures is small in small fields.
On the other hand the late Dr. Hopkinson has shown that, in fields
comparable with that of the earth and at a high temperature,
the permeability of wrought iron may amount to 1 1 ,000. On the
whole, I do not think it absurd to suppose that the permeability of
the iron shell (if it exists) may be taken as 1,000.
The meteoric theory of the constitution of the earth suggests
the possibility of a shell of meteoric iron; and as this substance
contains nickel, and some alloys of nickel and iron are very slightly
magnetic, this possibility may be regarded as weakening the case
for the existence of the shell.
I can not find any record of a measurement of the permeability
of meteoric iron, and though I hope to supply this want, it will be
dangerous to argue from results obtained with a single specimen.
There are, however, a number of large iron meteorites in the
Natural History Department of the British Museum, and by the
courtesy of my friend, Mr. Fletcher, F. R. S., the keeper of the
minerals, I have been allowed to test their magnetic condition. I
found that they were all strongly polarized by induction as though
by the earth's field, and on turning some of the smaller specimens
upside down the direction of magnetization was reversed.
The largest of these specimens was the famous Cranbourne me-
teorite discovered near Melbourne, in Australia, which was exam-
ined in situ by Dr. Neumayer in 186 1. He found it to be strongly
magnetized as though by induction. It is magnetized as though
by induction in its present position. All the evidence, therefore,
points to the conclusion that meteoric iron is fairly soft and per-
meable.
Taking then the radius of the earth as 6,400 kilometers, and n
as 1,000, we get the following shell thicknesses in kilometers from
Table I :
TABLE II
It ' . I , I H I *
6'4 128 I 24 I 4*8
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124 A ' W. RUCKER [Vol. IV, No. 2.]
Now, remembering that the second of these is almost certainly
too large, we are justified in saying that the shell-thicknesses cal-
culated on several hypotheses (all of which are very rough) are of
the order of the mean depth of the ocean (4 km.), and that this
purely provisional and preliminary argument, on the whole, supports
the view that if the magnetic material required by Mr. Wilde has
a permeability comparable with 1,000, the effects he imitates could
be produced by a shell whose thickness does not differ very much
from the average depth of the ocean. Pending further measures
on the permeability of magnetite, it appears that iron is the only
known substance which will satisfy the requirements of the case.
Effects of Thermal Conductivity.
Up to the present, I have assumed that the thermal conductiv-
ities of the materials employed are but little different. Our argu-
ments, with this limitation, have pointed to the conclusion that if
the magnetic matter indicated by Mr. Wilde's model really exists,
and if the magnetic properties of bodies are approximately the
same under great and small pressures, the hypothetical magnetic
shell must itself be of iron. As the thermal conductivity of iron
is about thirty times greater than that of stone, a very large addi-
tion may be made to the possible thicknesses as above calculated.
The gradient of temperature in the iron shell will be thirty times
less than in the rock, and whereas the two faces of a stone shell
4 km. in thickness would differ by 148 C, the difference of tem-
perature if the shell were made of iron would be only 4*9° C. This
advantage might be to a certain extent neutralized by the fact that
the better conductivity of the iron would tend to equalize the tem-
perature of all parts of the shell ; but though this would smooth
off the effects of relatively small elevations or depressions, it can
easily be shown that it would not affect large areas.
Taking a special case, consider an infinite solid, bounded by a plane
surface towards which there is a gradient of temperature of 37 ° C.
per kilometer. At a depth of 4 km. the temperature would be
148 C. Superpose, on this system, at the depth of 4 km. a variation
of 'temperature which, measured parallel to a given line (X) in the
surface, is given by the formula :
74 { sin ~ — 1 J
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EARTH'S SECOND A R Y MAGNETIC FIELD 1 25
Hence, there will be alternate maxima of 148 C. (the original tem-
perature of the layer) and minima of o° C, the transition being
very gradual, in accordance with the simple harmonic law.
We can make the change as sudden as we please by using (with
an appropriate constant in the place of w ) more and more terms of
4
the formula:
74X4 f * .sin irx , . sin $ttx t sin ^ttx \
~ir~ \ T+ 'x^ * x + 4 ~x — r.--| •
Taken to infinity, the Fourier series is — between x=o and x=tt
4
and — - between x=7r and x~2tt; i. e. % it represents alternate hot
and cold regions of breadth X, with discontinuities between them.
It will be sufficient for our present purpose to take the simpler
form, which includes only the first term. We shall therefore have
a distribution of temperature in the solid given by the formula:
f=i4*+37J'+74 I \Ae A +Be A isin ^— 1 j
Where y is measured in km. positive downwards from the place
4 km. below the surface, and A and B are arbitrary constants sub-
ject to the condition A+B=i. In the case considered, A=o and
B=i.
Next, replace the portion of the matter contained between y x
and y 2 by a material the thermal conductivity of which is thirty-
fold greater than that of the rest of the solid. As y is measured
from a plane which is itself 4 km. below the surface, the whole of
the new material is below the magnetic floor, as previously defined.
It is easy by well-known methods to find the temperature under
the new conditions in all parts of the compound solid.
It is sufficient to consider the lower surface of the plate, which
we will suppose to be at a depth y 2 from the bottom of the mean
ocean. If the whole solid were of uniform material the potential
at this depth due to the harmonic distribution of temperature
would be:
74* sin
X TTX
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126 A. W. RUCKER [vol. iv, No. a.)
After the introduction of the plate, it is
74 ^ <r sin v
where
B = _ 4 * _
2 (*r — *r 2 ) (* 2 — o + (* + o a - <j * 2 - 2 (* — o*
and if ^ is the depth of the upper surface of the plane,
£ ! — e ( t = e and k is the ratio of the conductivity of
the plate to that of the remainder of the material.
Hence, the difference between the maximum and minimum tem-
peratures at this depth when the solid is uniform, or is disturbed
by the introduction of the plate is :
2 x 74*r o — *.> •
Now it is evident that this difference of range is affected oppo-
sitely by two causes; firstly, the thermal resistance between the
surface of the solid and the lower surface of the plate is diminished
by the introduction of the plate, which will tend to increase the
range of temperature at the lower surface; secondly, the exchange
of heat between different parts of the plate is facilitated, which will
tend to reduce that range.
The first effect will be more prominent if the upper surface of a
thin plate is very near the surface of the solid ; the second will be
predominant if the plate is at such a depth that its thickness does
not materially facilitate the passage of heat to the lower plane.
Now, B 3 — i when ( l —( 1 , or (]=(k+i) (k—i). It is only, there-
fore, when the upper surface of the plate is at a depth greater than
that given by this limit that the range of temperature at the lower
surface will be adversely affected by the lateral conductivity of the
plate.
In the case under consideration, £=30, and if we take A'=3,6oo
km., or about 2,200 miles, we shall have alternate strips of " con-
tinent" and "ocean" of that breadth. Hence, B 2 =\ when
e 2ir yy^ 6oo =$i/29\ i. e. y when ^=38 km.
Hence, as this depth is greater than that at which we should
place the upper surface of the plate, we find that its presence in-
creases the range of temperature at its lower surface. For other
terms of the Fourier series the limiting value of j\ would be di-
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EARTH'S SECONDARY MAGNETIC FIELD
127
minished in proportion to the exponents of e; i. *., for the three
next terms it would be 12.6, 7.6, and 5.6 km. respectively.
As these depths are less than that at which the upper surface
of the plate need be placed, the indirect conductivity effect of these
terms will tend to equalize the temperatures of different parts of
the plate ; but they also tend to increase the average difference be-
tween the sub-continental and sub-oceanic regions.
It is hardly necessary to elaborate the point further ; but if we
take ^=18 and y 2 =2 7 km., tne depths of the boundaries of the
plate below the surface of the globe are 22 and 31 km. respectively.
Their temperatures will be 8i4°C. and 1,147° C, if the material
were rock; and 814° C. and 825° C. only, if the plate were iron.
Superpose at the depth of 4 km. the variation given by the formula
74 {^sS- 1 } •
This, added to the temperatures due to the vertical flow of heat,
makes the maximum temperature under the continent 148° C, and
the minimum under the sea o° C. If the material were uniform,
the temperature variation at 27 km. would be :
— 277r/^, 600 irx irx
74 e ' / o> sin -— — =72 sin- , - .
3,600 3,600
The introduction of the iron plate does not modify this to an im-
portant extent, and thus the temperature of the lower surface as
given by the formula :
825+72 ( sin ~_i )
3,600
giving, for mid-continent, shore line, and mid-ocean, the values 825°,
753°, and 68 1° C, respectively. At the upper surface, these would
all be diminished by about 1 1 ° C.
If we take the 742° C. as the temperature of non-magnetization,
it will cut the lower plane at the point where
7TX 1 1
sin —r--= — -0.15 .
3,600 72
Hence, *— 170 km., or, say, no miles. To this distance must be
added that due to the fact that the permeability will not reach its
maximum value until a certain temperature above 742° is attained,
so that perhaps a range of 200 or 300 miles in which the magnetic
part of the shell thickens and increases in permeability, and by
which edge effects will be smoothed off.
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I2 8 A. W. RCCKER [vol. iv, No. 2.]
On the whole, then, even if the approximate thicknesses calcu-
lated from the consideration of the shielding of complete shells are
too small, the additional range of thickness conferred by the con-
ductivity of the iron, would probably do away with all difficulties
as to the possibility of introducing a shell of the requisite shielding
efficiency above the magnetic floor.
Lamination.
One other point may be noticed. Under certain circumstances
the shielding effect of a spherical shell is improved if it is divided
into two concentric shells separated by a spherical crack, and in-
jured if the gap is filled up with magnetic material. (In the lec-
ture this was illustrated by coaxial cylinders filled with iron fil-
ings.) Thus, if a x and a are the external and internal radii of a
spherical shell, lamination will be injurious if
where ^ is a function of the permeability fi of the form
(2/i-fl)(M + 2)
= 9/2/i, if /x is large.
If the external radius and the amount of shielding material are
given, it may be better to divide the shell into two shells before
the thicknesses given by the above formula are reached, but a bet-
ter result can always be obtained by filling up the gap with the
magnetic matter until the limit given by the equation,
a 9
-^ = (1. -f \ f ) 2 is attained.
For thicker shells than those whose inner radius is given by this
formula it is positively injurious to fill the whole of the shielding
space with the permeable material.
Below this limit, lamination must diminish the shielding.
Now if ft = 1,000 ^ = 0*0045
• '. (1 + $)Y* = i'ooi5
& (1 + v~f) 2 A = 1*045
Hence, the advantage of lamination, when the quantity of ma-
terial is restricted, would begin, in the case of the earth, when the
thickness was about 10 kilometers; and, if the quantity is not re-
stricted, when the thickness is about 270 kilometers.
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EARTH'S SECONDARY MAGNETIC FIELD
129
These results would not hold good for a pierced shell ; but they
are sufficient to show that, with thicknesses such as those to which
we should probably be restricted in an accurate solution of the
problem, no great advantage is likely to be gained by the use of the
principle of lamination.
Summary.
The result of the foregoing discussion may be briefly summa-
rized as follows :
Mr. Wilde has produced a good magnetic model of the globe by
means of an arrangement which consists in effect of a primary
field due to a uniformly magnetized sphere, and a secondary field
due to iron placed near the surface and magnetized by induction.
The principal part of the iron is placed under the oceans; but evi-
dence is not forthcoming as to how far the close agreement between
the natural and artificial agonic lines and magnetic equators is due
to certain " polarizing strips " which were placed under the land.
Mr. Wilde attaches the greatest importance to the covering of the
oceans with iron.
As the result of a purely preliminary discussion it appears that
unless great pressure profoundly modifies the properties of mag-
netic matter, and subject to further experiments on the permeability
of magnetite, the material represented in Mr. Wilde's model by iron
can not be basalt or magnetite, but must be iron.
If once it be granted that an iron shell may exist within the
earth, there seems a priori to be no insuperable physical objection
to the hypothesis that it may be of the thickness requisite to pro-
duce the secondary field of the earth, and yet at temperatures be-
low that which would make it non-magnetic under ordinary
pressures.
The low temperature of the ocean bottoms affords an adequate
explanation of the difference of the magnetic properties of the
hypothetical shell below the ocean and the continents respectively.
Finally, the whole investigation has been conducted on prelim-
inary lines ; not with the intention of attempting to decide any of
the questions at issue, but with the view of determining whether
they are worth discussing. The general impression left upon my
own mind is, that though the fundamental hypotheses are beset
with difficulty, they do not tend to any obvious absurdity, and that
the relation between the permeability of the globe and its more
pronounced geographical features is worth further attention.
9
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REMARKS UPON PROFESSOR RUCKER'S PAPER AND
WILDE'S MAGNETARIUM.
By L. A. Bauer.
I am constrained to add a few remarks upon the foregoing paper
and the interpretation to be put upon the results derived from the
" Magnetarium." Professor Riicker admits that Wilde's results
must be received with great caution, and that the conditions under
which the experiments were performed are open to legitimate criti-
cism. As I have already had occasion in another connection to
point out some of the errors to which " the Magnetarium " results
are liable, I shall not enter again upon this matter, but simply accept
Wilde's observational results as correct, and endeavor to show what
interpretation is to be put upon them.
As Professor Riicker states, " The magnetic field of the earth
may be regarded as that primarily due to a uniformly magnetized
globe disturbed by some secondary causes." Furthermore, the
result of recent investigations has been that this field originates
practically from causes within the earth's crust, and can be referred
to a potential. The total magnetic potential on the earth's surface
can then be represented by the following terms :
V=V S + V' s + V u ; V S ^V P + V, ; V' s = V' p + V' e .
V s + V's together represent all that portion which can be referred
to a uniform magnetization about some diameter inclined to the
earth's rotation axis, V' s being that portion which can be regarded
as induced by V s . We can resolve V s and V' s each into two com-
ponent parts, one symmetrical about the rotation axis, Vp and V'p,
and the other symmetrical about diameters in the equatorial
plane, viz., V e and V' e% respectively. The ratio of (Vp + V'p) to
( V e + V'e) is nearly as 5 to i.
The problem now is to determine V u , the unsymmetrical por-
tion of the earth's magnetism ; i. e., that portion which can not be
referred to a simple magnetization about a diameter of the earth,
and to ascertain the causes producing the unsymmetrical magnetiza-
tion. The general assumption amounts to this : the earth has a
symmetrical primary field ; secondly, a symmetrical secondary field ;
and. thirdly, an unsymmetrical secondary field. It is then very
evident that the accurate determination of V u depends upon the
accurate elimination of the symmetrical portion, V' s + V s .
Now, in the present state of our knowledge, we can build up
the symmetrical field in an infinite number of ways. Wilde has
done this in one way. He starts with a primary resultant field, ap-
proximately, tuned to one station, London. He finds that this field
does not yet represent the general magnetic phenomena. After
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WILDE'S MAGNETARIUM 1 3 1
various trials, he covers the ocean areas (three-fourths of the earth's
surface) with sheet-iron, adds polarizing bands over the land areas
here and there until he has obtained some of the striking magnetic
phenomena. He then concludes that the primary cause of the un-
symmetrical distribution of the earth's magnetism is to be referred
to the fact assumed; viz., that the earth beneath the oceans is more
highly magnetizable than that beneath the continents.
When Wilde covers almost the entire earth (over three-fourths)
with sheet-iron, he hasladded practically a third field to his two pri-
mary ones, the effects from which would consist largely of another
symmetrical magnetization. In other words, before covering the
ocean areas with sheet-iron and adding the various polarizing bands
over land areas, he had not yet succeeded in obtaining even the
phenomena of the symmetrical portion of the earth's magnetism.
The amount and disposition of the sheet-iron pieces depend entirely
upon the primary fields we start with. Having no means at present
for deriving the precise primary field, we may start in an infinite
number of ways and get an infinite number of arbitrary results. It
is, therefore, apparent that we can not as yet accept the validity of
Wilde's conclusion as to the cause of the iinsymmctrical distribution
of the earth's magnetism.
Professor Riicker has pointed out, by an example, that it is ?iot
sufficient to reproduce only certain ones of the observed magnetic
phenomena. / have no hesitation in asserting that, if an independent,
unbiased investigation is made of the results of the Wilde Magnetarium
for the various elements of the earth's magnetism, certainly just as
many, if not more, discordances as accordances will be found between
the actually observed results and the Magnetarium results. The same
conclusion I reached some time ago with regard to his secular vari-
ation results.
Reference has been made in the previous article to my residual
field as illustrated in the paper in the March issue of the Journal.
My published map is based, not only upon certain observed features
of the earth's magnetism over certain regions, but upon all the ob-
served elements at 1,800 points symmetrically distributed over the
earth's surface between latitudes 6o° N. and 6o° S. All that portion
(whether due to inducing or to induced fields) which could be referred
to a uniform magnetization about a diameter inclined to the earth's
axis was first eliminated. I accepted for this purpose, Schmidt's
results as derived from his elaborate investigations. The first-order
terms of the Gaussian expansion will not necessarily give the
maximum amount of the earth's magnetism that may be due to such
a simple magnetization, and so, some years ago, I made a prelim-
inary investigation towards ascertaining how much the result from
the Gaussian expansion would differ from the maximum result, and
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132 L. A. BA&ER [vol. iv, no.*.]
found it to be very small. I shall enter upon this matter more fully
in my next paper, and likewise deduce some interesting facts per-
taining to the symmetrical field. The only point I desire to make
here is, that my residual field is not that which Wilde gets when he
adds the sheet-iron coverings and bands; for, as shown above, in his
field there lurks still a large part of symmetrical magnetization.
My residual field does not reveal the fact that the cause of the
unsym metrical distribution is due to the earth under the ocean areas
being more magnetic than below the continental areas. It does show,
however, apparently, that the primary cause of the unsymmetrical
distribution is connected in some manner with the distribution of
land and water; for, after a careful comparison made by myself and
others, the final conclusion reached was, that the "unsymmetrical
distribution of the earth's magnetism and the unsymmetrical distri-
bution of temperature as exhibited on the earth's surface, on the
average for the year, are in some way related to each other." I was
careful not to say that one was the cause of the other, although some
facts revealed might have warranted such a conclusion. I prefer to
leave the assigning of the cause open as yet ; for both phenomena,
the unsymmetrical temperature distribution and the unsymmetrical
magnetic distribution, may not necessarily be connected with each
other as cause and effect, but may both be effects from the same
cause; viz., the distribution of land and water, ocean currents, etc.
Hence, the guarded way in which I formulated my conclusion.
That there certainly is a remarkable similarity between the map of
the isabnormal temperatures and that of the residual magnetization;
a careful inspection will show.
Professor Riicker points out an objection to the possibility of
such a connection ; viz., that the " deviation of the average temper-
ature of any points at the surface of the ocean from the average for
the corresponding latitude is a surface phenomenon, which, at points
near the bottom of the ocean, is completely masked by the influx of
cold water." The annual isabnormal temperatures may be regarded
as referring to a layer at a depth beyond the influence of the diurnal
and the annual temperature variations, say about 50 to 60 feet on
the average. Professor Riicker forgets that the magnetic elements
which we are compelled to deal with are also surface phenomena.
We know absolutely nothing of the actual distribution of the mag-
netic elements at the bottom of the oceans. Here is a wonderful
opportunity for scientific investigation ! However, that great tem-
perature differences are bound to exist along parallels of latitude at
the average depth of the oceans is a well-known fact. It does not
seem to me, therefore, that Professor Rucker's objection is as yet a
valid one.
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.-f.
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(Plate IV.]
<zj£*^^
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/ BIOGRAPHICAL SKETCH OF DR. JOHN LOCKE.
By L. A. Bauer.
The city of Cincinnati has the honor of having taken a leading part
in the inauguration in this country of scientific work in astronomy,
meteorology, and terrestrial magnetism — in astronomy, through the
labors of Mitchell, the founder of the Cincinnati Observatory ; in mete-
orology, through the vigorous impulse given to the science by Professor
Cleveland Abbe, when he was director of the Cincinnati Observatory;
and in terrestrial magnetism, through the enthusiasm and zeal of Dr.
John Locke.
I propose to speak here especially of the work of Dr. Locke, who was
one of the foremost of the pioneers in terrestrial magnetism in this
country. Through the kindness of his son, Colonel Joseph Morris Locke,
who resides in Cincinnati, and whose acquaintance I have had the priv-
ilege of making, I am enabled to give the excellent portrait of his father
herewith reproduced.
Professor John Locke, M. D., was born in Lempster, New Hampshire,
February 19, 1792. He was a descendant of William i/ocke, who sailed
from London, England, in the ship Planter,. April, 1635, for the Massa-
chusetts Colony, and in line of descent from whom was Samuel B. Locke,
president of Harvard University. Collateral branches furnished pro-
fessors to Dartmouth College and other schools of learning.
His grandfather, father, and brother had a fine reputation in New
England as expert engineers and millwrights, or hydraulic engineers, as
they would now be called. The family had for a time no settled home,
but moved about from place to place wherever the father's business
called him. They finally settled at Bethel, on the Androscoggin River,
in Maine.
His father had a very good private library for those days, which was
a great help and incentive to his son. When the youth had exhausted
all local means of obtaining an education, he desired to carry on his
studies elsewhere. This desire his father opposed, as he wished him to
take up his own profession of millwright. Locke was thus obliged to con-
tinue unaided his efforts to obtain an education. For a while he was an
assistant in Professor Silliman's laboratory at Yale. Later he was curator
of botany in Harvard. In 18 18, he was appointed assistant surgeon in the
United States navy. In 18 19, he graduated in medicine at Yale College.
In 1 82 1, he went to Kentucky and organized an "academy for
females " at Lexington. The following year he removed to Cincinnati,
where he established the " Cincinnati Female Academy." In 1825 he
married a favorite niece of the late Nicholas Longworth, of Cincinnati.
Ten children were born to them, four of whom are still living — two sons
and two daughters. In 1835, he was appointed professor of chemistry
and pharmacy in the Medical College of Ohio, which chair he occupied
with signal success for eighteen years.
In 1837, Dr. Locke visited Europe, where he was cordially received
by scientific men. On his return to this country, he was connected for a
time with the first geological survey of Ohio. In 1839, he was appointed
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134 £• A. BAUER [vol. iv,no.m
upon the United States geological exploration of the mineral lands of
Iowa, Wisconsin, and Illinois. At Philadelphia, April, 1840, in connection
with others, he organized the American Association of Geologists and
Naturalists, and presided at many of its meetings. This Association,
by gradually incorporating other branches of science, developed into the
present American Association for the Advancement of Science.
From 1838 to 1848, Dr. Locke devoted a great deal of labor to per-
fecting a^connected survey of the magnetic dip and intensity of the
northern portion of this country. In recognition of his labors in this
connection, the British Government, at Sabine's suggestion, presented
him with a magnetometer and theodolite by Meyerstein of Gottingen. 1
In 1848, he perfected his invention of what he first called the "Auto-
matic Clock Register;" later he created for it the word chronograph,
which is the term now in use. In 1849, in recognition of Dr. Locke's
services to science and his invention of the chronograph, Congress ap-
propriated $10,000, at that time a munificent sum.
He resigned his position in the Ohio Medical College in 1853. The
following year he moved to Lebanon, Ohio, but returned to Cincinnati
in 1855, much broken in health. He died on July 10, 1856, at the age of
sixty^four years.
Dr. Locke made notable additions to our knowledge in various
sciences. His unselfish devotion and many valuable contributions to
the science of terrestrial magnetism certainly deserve more than the
passing notice we can here give them. His investigations and magnetic
surveys from 1838 to 1848 extended from the southern part of Kentucky to
the northern side of Lake Superior, and from the State of Maine to some
distance beyond the Mississippi. They were conducted almost entirely
at private expense and with an enthusiasm and zeal worthy of the cause.
His observations were the first to give indication of the situation of the
American focus of greatest magnetic intensity, his results being verified by
the later investigations of Lefroy. His excellent investigation of the local
deflections of the magnetic force, as exhibited notably at the Palisades of
the Hudson, constitute a valuable contribution to our knowledge of the
subject. Without more careful research, for which we at present have
not the time, it would be difficult to say who, among the early " magnetic "
pioneers of this country, has the honor of having made the first absolute
(or even differential) determination of the magnetic intensity.
He proposed to make Cincinnati the base of reference of a magnetic
survey of the United States, and calling the value of the earth's horizontal
force at Cincinnati unity, he determined the horizontal intensity in terms
of this unit at stations in the United States, Canada, and Europe.
All honor to the British Government and Colonel Sabine that, when
Dr. Locke's appeal for aid from American societies then in existence could
not be responded to, they saw their way clear towards supplying him
with the desired instruments, and thus, by their recognition of the value
of his labors, gave him the stimulus and encouragement so desirable to
every true investigator of nature's secrets !
1 These instruments, as also others, are now in possession of Colonel Joseph M.
Locke, of Cincinnati, who also has many of his father's books and private papers.
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MEAN VALUES, FOR THE YEARS SPECIFIED, OF THE MAGNETIC ELEMENTS
AT OBSERVATORIES WHOSE PUBLICATIONS ARE RECEIVED
AT KEW OBSERVATORY. 1
Intensity
Place
Latitude
Longitude
Year
Declination
Inclination
(C. G. S. Units)
Hor'l
Vert'l
o /
/
/
/
Pawlowsk
59 41 N
30 29 E
96
21 3 E
70 41 6 N
•16495
•47084
Kathari nenburg
56 49 N
60 38 E
96
9 47 *5 E
70 40 *o N
•17811
50765
Kasan
55 47 N
49 8 E
92
7 30 '» E
68 36 -2 N
18551
•47345
f
95
10 35 3 W
68 47 N
17400
•44821
Copenhagen
55 41 N
12 34 E \
96
10 29 *5 W
68 45 -6 N
•17422
•44824
{
97
10 24 -4 W
68 43 •« N
•i745o
•44826
Stony hurst
53 5i N
2 28 W
97
18 27 6 W
68 53 9 N
•17236
•44663
Hamburg
53 34 N
10 3 E
96
11 36 7W
67 38 -8 N
•18061
•43921
Wilhelmshaven
53 32 N
8 9 E
97
12 41 6 W
67 49 N
•18028
•44213
Potsdam
52 23 N
13 4 E
97
10 9 7 W
66 36 3 N
•18775
•43398
Irkutsk
52 16 N
104 16 E
96
2 5 -2 E
70 11 *8 N
20139
•55929
Utrecht
52 5N
5 11 E
96
14 9 7 W
67 4 5 N
•18448
•43618
Kew
51 28 N
19 W
98
17 1 4 W
67 17 6 N
J 67 7 'iN|
1 67 6'5Nj
•18364
•43885
Greenwich 2
51 28 N
1897
16 50 4 W
18387
J '43567
I '43546
Uccle (Brussels)
5048 N
4 21 E
1897
14 27 -3 W
66 19 5 N
•18917
43145
Falmouth
50 9 N
5 5W
1897
18 42 2 W
•18595
—
Prague
5o 5 N
14 25 E
1897
9 21 'i W
•19884
—
St. Heher
(Jersey)
49 12 N
2 5W
1898
17 7 *9 W
65 52 -5 N
—
—
Pare St. Maur
(Paris)
48 49 N
2 29 E
1896
15 3 *9 W
65 1 '6 N
19685
•42264
r
1895
8 39 '3 W
63 9 N
20731
40951
Vienna
48 15 N
16 21 E i
1896
1897
8 33 *8 W
8 28 -i W
63 7 1 N
•20756
•20785
40944
I
1898
8 24 1 W
•20797
—
O'Gyalla (Pestli)
47 53 N
18 12 E
1896
7 46 9 W
•2 1 105
—
Odessa 3
46 26 N
3° 46 E
1897
4 47 '3 W
62 30 -9 N
•22039
•42372
Pola*
44 52 N
13 5i E
1897
9 36 -6 W
60 28 N
•22088
38967
Nice
43 43 N
7 16 E
1897
12 18 8 W
60 i 5 4 N
•22318
•39059
Toronto
43 40 N
79 30 W
1897
4 53'oW
•16650
Perpignan
42 42 N
2 53 E
1896
13 55 '3 W
60 5 - 9 N
22398
•38948
Rome
41 54 N
12 27 E
1891
10 45 *i W
58 4 6 N
•2324
•373o
Tiflis
41 43 N
44 48 E
1896
1 53 7 E
55 48 'I N
•25670
. '37775
1
1894
9 41 7 W
—
—
Capodimonte
1895
9 37 W
56 37 9 N
•24007
•36454
(Naples)
40 52 N
14 15 E ]
1896
9 32 1 W
56 37 1 N
•24040
•36484
1897
9 26 3 W
56 31 4 N
24075
•36406
Madrid
40 25 N
340W
1895
16 6'6W
—
Coimbra
40 12 N
8 25W
1896
17 36 8 W
59 40 *2 N
•22620
•38662
Washington
38 55 N
77 4W
1894
3 39 '9 W
7o 34 3 N
•19979
56646
(
1896
17 35 '9 W
58 11 8 N
23346
•37648
Lisbon
38 43 N
9 9W
1897
17 3i *W
58 8 -2 N
•23385
37624
I
189S
17 27 7 W
58 7-8N
■23413
•37660
Zi-ka-wei
31 12 N
121 26 E
1895
2 15 6 W
45 55 'I N
32679
•33743
Hong Kong
22 18 N
114 10 E
1897
23 .3 E
3i 36 '9 N
36547
22497
Tacubax a
19 24 N
99 12 E
i8 9 >
7 45 '6 E
44 22 2 N
•33428
•32764
Colaba (Bombay)
18 54 N
72 49 E
1896
33 '8 E
20 55 -6 N
•37463
14326
Manila
14 35 N
120 58 E
1896
51 E
16 39 7 N
•37868
•1 1333
Batavia
6 11 S
106 49 E
1896
1 22 E
29 29 5 S
36768
•20795
Mauritius
20 6 S
57 33 E
1896
9 48 7 W
54 32 .3 S
•23913
•33572
Melbourne
37 50 S
M4 58 E
1896
8 15 -o E
67 18 -3 S
•23392
55936
1 Compiled by Dr. Charles Chree, and published in Proc. 0/ Roy. Soc. for 1899.
2 Of the two values of the Inclination and Vertical Intensity, the first is based on observations
with 3-inch dip needles only, the second on combined observations with needles of 3, 6, and 9 inches.
3 Inclination and Vertical Intensity means from six summer months.
« Inclination and Vertical Intensity means from five months, January-May.
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NOTES
/
CHARLES A. SCHOTT.
It gives us great pleasure to be able to present to our readers, in
this number, the portrait of the well-known American magnetician,
Mr. Charles A. Schott.
Mr. Schott was born at Mannheim, Baden, Germany, August 7, 1826.
After passing through the public school and partly through the Ly-
ceum of his native town, he entered the Polytechnic School at Carlsruhe,
where, after a six-year course, he graduated as civil engineer in 1847.
There being no immediate prospect of employment by the State, he
asked for leave to visit the United States of America, where he arrived
in August, 1848.
In December of that year he entered the service of the United States
Coast Survey, and in due time became a citizen of the United States.
Being at first engaged in office and nautical duties, he was assigned to
the position of Chief of the Computing Division of the Survey in 1855,
a place he still occupies, and was advanced to the grade of Assistant
in 1856.
His numerous contributions to the annual reports of the Survey
since 1854 relate to hydrography, geodesy, practical astronomy, and
especially to terrestrial magnetism. He has also published through the
medium of the Smithsonian Institution, between the years 1858 and 1881,
a number of memoirs bearing on meteorology, and on subjects relating
to Arctic Explorations. He was a member of the Government parties
sent to Springfield, Illinois, to observe the solar eclipse of August, 1869,
and to Catania, Sicily, to observe that of December, 1870. As delegate
from the United States Coast and Geodetic Survey, he attended the Inter-
national Conference of Magneticians, held at Bristol, England, in con-
nection with the meeting of the British Association for the Advancement
of Science.
Mr. Schott was elected a member of the National Academy of Sciences
in 1872, and is a member of the Philosophical Societies of Philadelphia
and Washington ; the American Association for the Advancement of
Science ; the Academy of Sciences of Catania, Sicily ; the Sociedad Cien-
tifico Antonio Alzate, Mexico, etc.
Last year he received the Henry Wilde prize of 4,000 francs from the
Academy of Sciences of France, for his numerous contributions to ter-
restrial magnetism.
136
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XOTES 137
ACTIVITY IN MAGNETIC WORK.
Notice to Correspondents.— Correspondents and subscribers are ear-
nestly requested to take note of change of address, as elsewhere given, of
publisher and of editor.
Reprinted Edition of Volume I. — By reprinting portions of Volume I, we
are again enabled to make up a few complete sets. Those whose sets are in-
complete will do well to attend to this matter at once. For prices, see adver-
tisement
Grant from the Smithsonian Institution to the Journal — In view of the
addition of atmospheric electricity to the scope of the Journal, the current
volume is published with the assistance of an allotment from the Hodgkins
Fund of the Smithsonian Institution.
Professor Max Eschenhagen has just made a series of comparisons of
his magnetic instruments with those at the Pola Magnetic Observatory, the
results of which will be given in a future number.
Professor Joseph Liznar, formerly Adjunct at the "Central Anstalt fur
Meteorologie und Erdmagnetismus " at Vienna, resigned his position on Feb-
ruary 1st, in order to accept the professorship of Meteorology at the Royal
Agricultural College of Vienna. We trust that in this position he may have
opportunities for carrying on the work in terrestrial magnetism in which he
has been so successful in the past.
Dr. L. A. Bauer resigned his position as Assistant Professor of
Mathematics and Mathematical Physics at the University of Cincinnati on
May 1st, in order to accept the position of Chief of the newly- formed Divis-
ion of Terrestrial Magnetism of the United States Coast and Geodetic Sur-
vey. His duties will consist in the administration of the office work and the
inspection of the field and observatory work in terrestrial magnetism. He
has likewise been appointed Lecturer in Terrestrial Magnetism at the Johns
Hopkins University. The Journal will hereafter be issued from the Johns
Hopkins press.
Magnetic Observatory at Vienna. — The magnetic observations at this Ob-
servatory have had to be entirely discontinued on account of the pernicious
effects from electric tramways and electric-light wires. We understand that
the Director of the Observatory, Professor Pernter, has submitted a plan to
the Austrian Government for a new Observatory, to be situated some distance
from Vienna, and to be provided with instruments of the latest construction.
We trust that Professor Pernter's plan will be carried out.
Batavia Magnetic Observatory \ Java. — Under date of February 2, 1899,
Dr. W. van Bemmelen, the Assistant Director of the Batavia Magnetic and Me-
teorological Observatory, informs us that, in all probability, the magnetic
work at this Observatory will be vitiated to a great extent, in the future, by
the close approach of electric tramways. On account of the valuable mag-
netic work carried out by this Observatory, every magneticain will regret to
receive this information. Should the threatened danger prove as serious as
10
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138 NOTES l vol. IV. No. 2]
expected, the magnetic work will have to be carried out during only the
night hours, when the tramways cease running. Dr. van Bemmeleu in-
forms us also that his revised isogonic charts, at the time of writing, were
passing through the press.
Magnetic Effect from Electric Tramways, — Professor Eschenhagen, un-
der date of April 28th, sends the following preliminary notice regarding the
results of the investigations of the magnetic effect from electric tramways :
"Die Bearbeitungen unserer Beobachtungen in der Nahe electrischer
Bahnen durch Herrn Dr. Edler sind nun fertig gestellt Das Resultat ist, dass
die Stoning abnimmt mit der ersten Potenz der Entfernung, also nicht mit
dem Quadrate. Dies bedeutet, dass die vagabundirenden Strome sich in einer
Plache ausbreiten. Es kann natiirlich nicht gesagt werden, ob dies in jedem
Terrain der Fall ist In dem untersuchten, sandigem Oebiete stand das
Grundwasser sehr hoch, moglicherweise ist es auf Felsen anders."
A fuller report will be given in a future number.
Magnetic Observatory at Pola. — The only Observatory in Austria at which
complete registrations of the magnetic variations are now being made is the
one at Pola, belonging to the Hydrographic Department of the Austrian -
Hungarian Navy. The Division of Geophysics of this Department has been
reorganized by Line-Lieutenant W. Kesslitz, and has published, since 1896, an
admirable year-book, containing the results of the magnetic and the meteor-
ological observations.
Mr. James B. Baylor ; Assistant in the Coast and Geodetic Survey, is at
present engaged upon the magnetic survey of North Carolina, the expense
of which is being borne conjointly by the State Geological Survey (W. H.
Holmes, State Geologist) and the Coast and Geodetic Survey.
Magnetic Survey of Maryland.— Dr. Bauer spent about four weeks, dur-
ing May and June of this year, in making magnetic observations at such points
in Maryland where the distribution of the earth's magnetism is very irregu-
lar. The "Second Report Upon Magnetic Work in Maryland" is now passing
through the press. The expense of the magnetic work is being borne con-
jointly by the State of Maryland and the Coast and Geodetic Survey.
Instruction in Terrestrial Magnetism at the Massachusetts Institute of
Technology, Boston, Massachusetts— -We note with pleasure that this pro-
gressive institution has made the proper provisions and provided the neces-
sary quarters, far removed from disturbing influences, for the instruction of
students in the making of magnetic observations. The endeavor will be
made to carry out work of permanent value, and in co-operation with the
Coast and Geodetic Survey.
The new Coast and Geodetic Survey steamer, Pathfinder, in her cruise
this summer from Washington to Alaska, by way of Strait of Magellan, will
make magnetic observations at various ports in North and in South America.
The intention is to observe at statious previously occupied. Mr. F. W.
Perkins, Assistant of the Survey, is in command.
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ABSTRACTS AND REVIEWS
MAGNETIC OBSERVATIONS IN THE PHILIPPINES. 1
In an historical introduction the author relates that the three elements*
declination, inclination, and horizontal component, were determined at Manila
as early as 1840. The declination was determined at Zamboanga on the nth
day of April, 1885, and found to be i° 35' E. In the year 1889 a fire destroyed
many valuable magnetic records.
The first complete installation in these Oriental regions, making use of
photography for the study of magnetic variaiions and perturbations, is due to
the Mission of the French Jesuits of Zikawei, China, near Shanghai, where a
maguetograph has been in operation since the year 1877. The magnetic de-
partment of the Manila Observatory dates from the year 1877. It was founded
under the direction of the enthusiastic magnetician, P. Martin Juan, who, in
preparation for the work, had spent one year in the Magnetic Observatory at
Stonyhurst, England, and later some time in France, where he determined
the constants of the instruments just purchased for the Manila Observatory.
These instruments, a theodolite compass and an inclinometer, were like those
used in the magnetic survey of France by Moureaux.
On his arrival at Manila, P. Juan instituted a regular series of absolute
magnetic observations, and a set of instruments for recording the variations
was obtained by him from Carpentier, at a cost (including accessories) of about
|5,oco. In the following year, 1888, a scientific commission was authorized to
determine the magnetic elements in the southern islands, and P. Juan set out
on an expedition for this purpose. After making observations at several
points, he was suddenly taken down with fever, induced by undue exposure
to the rays of a tropical sun, and a few days later he died. His death occurred
in July, 1888, at Surigao, on the Island of Mindanao. At the early age of
thirty-eight his life was thus cut short in the beginning of a devoted and
promising career.
In July, 1889, the Manila Observatory received an Elliott Unifilar Magnet-
ometer and a Dover Inclinometer, these instruments being identical with those
in use at the Kew Observatory, and having been carefully compared with the
latter for the determination of constants. The Observatory now had two sets
of absolute instruments, and also two sets of instruments for the study of the
variations. ^
In the following year began the regular publication of observations and
registered perturbations, the magnetic section having been placed in charge
of P. Ricardo Cicera, the author of the volume under review.
A special building was erected for magnetic work, the piers and general
arrangements being modeled after those at Pare St. Maur in Paris. The con-
'El Magnetismo Terrestre en Filipinas. Por el P. Ricardo Cicera, S. J.,
Director de la Secci6n Magnetica, Observatorio Meteorologico de Manila, 1893.
22x31cm. Pp. x + 158 136*. Numerous plates.
139
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1 40 RE VIE WS [vol. iv, No. 2j
dition of the soil in the neighborhood of Manila renders it impracticable to
use a basement-room, which is desirable for uniformity of temperature. The
ground is so wet that water is found at a depth of two meters, even in the
driest season. During a great part of the year the rainfall is plentiful, and
water filters through the most compact walls.
On this account the installation was made above the surface of the
ground. The building was constructed of wood, with exclusion of iron ; the
foundation is composed of calcareous stone and cement Bricks were de-
barred as a building material, owing to their magnetic ingredients and on
account of danger from earthquakes.
In the year 1891 observations of declination and inclination were made
at Manila by the commander of an English warship, the results agreeing
within i' with those determined at the Observatory. In this same year a
commission was sent to China and Japan to determine the magnetic elements,
which work was successfully done in the face of considerable obstacles.
In 1892 another commission was appointed to trace the magnetic charts
of the Philippine Archipelago.
Detailed accounts are given of the several expeditions to different islands
for the prosecution of magnetic work. These accounts acquire additional
interest at the present time from the information incidentally given concern-
ing the climate, the winds prevailing in certain seasons, the rainfall, the
temperature, etc.
The tables give full details as to the results of observations ; the tracings
present valuable records of perturbations and variations ; the charts of iso-
gonic, isoclinic, and isodynamic lines are full of interest, though the work, as
planned, is only fairly begun.
Observations are recorded which were made during eclipses. No decisive
connection between solar eclipses and magnetic changes was established, but
additional confirmation is given of a relation between solar activity and mag-
netic perturbations, including the eleven-year period.
During eclipses of the moon there was noted a tendency of the needle to
deviate toward the west, the eastern declination undergoing a diminution.
The value of the horizontal component suffered a small augmentation during
a partial lunar eclipse on the 12th of May, 1892, rising during a period of four
hours from 0.37631 to 0.37668; during a total eclipse of the moon in the pre-
vious year a slight diminution in the value of H was observed.
University of Cincinnati, April, 1899. Thomas French, Jr.
Coast and Goedetic Survey. Distribution of the Magnetic Dip and Mag-
netic Intensity in the United States for the epoch, January 1, 1900, by C. A.
Schott. App. No. 1, Rep. for 1897. Washington, 1898. Pp. 161-196. and
3 charts. 23 x 29 cm. [Cf., p. 97.]
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REVIEWS I4 i
HARMONIC ANALYSIS OF THE MAGNETIC VARIATIONS. 1
In this paper the author describes the method which he, and a number
of other magneticians, have decided to employ for the harmonic analysis of
magnetic variations.
The daily variations of total intensity, T, of declination, <\ and of inclina-
tion, /, are to be represented by periodic formulae. The variations of the
rectangular components (north, east, nadir), X, V, Z, are therefore studied.
Only such published values of the variations are to be used, which are the
mean results of hourly observation throughout the month. The monthly
means of the variations from the daily mean, if not already given in the
publications, is found for every hour, for every month throughout the year.
The annual period is easily eliminated by a linear interpolation formula
(Lamont's). The mean variations for the entire year are also formed, and
more especially for the polar day and polar night. The author hopes thus to
be able to separate the direct from the indirect influences (temperature, etc.)
of the relative position of earth and sun. If observations of many years
are to be had, eleven-year means are also formed in order to eliminate the
eleven-year period.
The form adopted for the periodic formulae is —
/(■*) = u + ^ u m + s in {U m + mx) ,
xn=l
and a simple method is described for performing the numerical part of the
process.
From the results, as Schuster has first shown, may be answered the ques-
tion whether the causes for the daily variation are above or below the earth's
surface. The direct and indirect influences of the earth's position in space
may thus be separated. Also the geographical distribution of the values of
the coefficients may give rise to important discoveries, as, for instance, an
increase or decrease with the latitude.
The author hopes that all magneticians, interested in this work will enter
into correspondence with him. He has asked the reviewer to publicly ex-
press his appreciation to those that are already his collaborators, as well as
to those who may yet wish to assist in this important work.
University of California. E. J. Wii«czynski.
1 A. Nippoldt, Jr. Ein Verfahren zur harmonischen Analyse erdmagnetischer
Beobachtungen nach einheitlichem Plane. Annalen der Hydrographie. Februar,
1899. Pp. 57-64.
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142
REVIEWS [Vol IV, No. 2.)
Wild, H. Ueber die Bestimmung der erdmagnetischen Inclination und ihrer
Variationen. Vierteljahrsschrift der Naturforschenden Ge9ellschaft in
Zurich. XLIII. 1898. October. 22 S., 8°.
Verfasser giebt in dieser Abhandlung auf Grund eigener und anderer
Erfahrungen eine Kritik der Genauigkeit der zur Messung der Inclination
und ihrer Variationen dienenden Beobachtungsmethoden, die um so mehr
das Interesse aller erdmagnetischer Forscher verdient, als gerade das ge-
nannte Element von alien Bestimmungsstucken bis jetzt am unsichersten
gem es sen werden kann.
Was zunachst die absolute Inclination betrifft, so kommt Verfasser zu
dem Resultat, dass die Genauigkeit der Messungen mit dem Nadelinclina-
toriutn selbst der besten Construction hochstens auf ± 1' angenommen wer-
den kann. Die Erfahrungen zu Pawlovsk haben gezeigt, und Referent kann
dies auch bestatigen, dass einzelne Nadeln Veranderungen erleiden, die den
obigen Betrag noch uberschreiten.
Wesentlich gunstigere Resultate sind nun mit dem Inductions- 1 nclinato-
rium erzielt, insbesondere seit die urspriingliche Methode von W. Weber
derart modificirt ist, dass der Fehler, welcher aus der Ungleichheit der An-
schlage des Galvanometers bei verschiedenen Stellungen des Inductors ent-
springt, beseitigt wird. Dies geschieht bekanntlich am besten dadurch, dass
man entweder in symmetrisch zur Inclinationsrichtung gerichteten I^agen die
Drehungsaxe beobachtet,und gleiche Ausschlage erzielt, oder indem in einer
Anzahl von Lagen beobachtet, die jener Richtung benachbart und auf bei-
den Seiteu derselben liegen und dann aus den kleinen Ausschlagen die In-
clinationsrichtung durch Interpolation ableitet, oder drittens indem man
jene Lage, in welcher der Anschlag Null ist, direct aufsucht. H. Wild
hat nach der ersten Methode mit einem alteren Instrument die Genauig-
keit von ±0/06 erreicht und hofft mit einem neueren nach der letzten
Methode die Genauigkeit noch auf das Dreifache steigern zu konnen.
Nach der zweiten Methode beobachtete, wie Referent noch hinzufugen
mochte, Dr. Giese auf der Polarstation zu Kingua-Fjord 1883, nachdem K.
Schering in Gottingen zuvor den alten Weber'scheu Erdinductor mit giinsti-
gem Erfolg hierfur abgeandert hatte. Referent mochte gerade die Giese'sche
Reihe erwahnen, weil es die al teste langere Reihe von sicheren Beobachtun-
gen mit dem Erdinductor in hohen Breiten ist, die streng auf Normal stande der
Variationsiustrumente reducirt ist. Vielleicht ist es auch nicht uninteressant
hinzuzufugen, dass die altesten Beobachtungen nach dem urspriinglichen
Weber'scben Verfahren mit dem Erdinductor in arctischen Regionen von C.
Borgen und Copeland auf der 2. Deutschen Polarexpedition bereits im Jahre
1869 — 70 angestellt worden sind. Eine noch in Frage kommende Modifica-
tion des Erdinductors ist die in Potsdam gebrauchliche mit zwei gleichzeitig
in Rotation versetzten Spulen nach h. Weber. Nach den Verbesserungen die
an der urspriinglichen Form angebracht sind, glaubt Referent, dass sich eine
Genauigkeit von 0/1 — 0/2 erzielen lasst. Es ware leicht, dieselbe durch Be-
nutzung eines empfindlichen Galvanometers scheinbar zu steigern, doch halt
mit dieser Steigerung die Genauigkeit und Stabilitat der Orienttrung und
der Stromabnahme nicht Schritt. Referent kann auch das Bedenken nicht un-
terdriicken, dass die in diesen Umstanden liegenden Fehlerquellen auch die
voui Verfasser mit seinem Instrumente als erreichbar angegebene Grenze von
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REVIEWS
H3
1" illusorisch machen wird; ganz abgesehen da von, dass auch die Ablesung
der Inductoraxe an der Kreistheilung ebenso weit getrieben, also Fehler
der Kreistheilung etc. beriicksichtigt werden miissten. Auf jeden Fall
ist aber dem Verfasser beizustimmen, wenn er den Inductor als das sicherere
Instrument empfiehlt. Nur mochte Referent vorschlagen, doch die Verbes-
serung des Nadelinclinatoriums nicht aufzugeben, da die Controle. welche in
der Anwendung zweier auf so verschiedenen Principien beruhenden Instru-
mente liegt, eine nicht zu unterschatzende Sicherheit bietet.
Was die Iustrumente zur Bestimmung der Variationen der Inclination
bezw. Verticalintensitat betrifft, so findet Verfasser, dass zur Zeit die Lloyd'-
sche Wage allein ein befriedigendes Instrument ist ; dass indess doch der
Wunsch besteht, noch andere Methoden, z. B. Induction in einem dauernd
gedrehten Inductor einer Prufung zu unterziehen.
Die Erfahrungen mit der Lloyd'schen Wage scheinen nicht an alien Ob-
servatorien gleich giinstig zu sein, in Potsdam zeigen sich allmahliche Null-
punctsanderungen, noch starkere werden aus Pola und Odessa mitgetheilt, fiir
welchen Fehler eine constante Abnahme des magnetischen Moments wohl
nicht allein verantwortlich gemacht werden kann. Offenbar muss die Zu-
sammensetzung der mechanischen Theile der Wage eine sehr sorgfaltige und
dabei moglichst einfache sein.
Den Versuch Dr. Giese's die Induction im geschlossenen Stromkreise Va-
riationen der Vertical-Inteusitat zuerhalten, schlagt Verfasser zur Nachahmung
vor. Zur Zeit sind solche Versuche nach einem bereits im Deutschen Polar-
werke gemachten Vorschlage des Referenten im Gange, iiber die gelegentlich
einmal berichtet werden soil.
M. ESCHENHAGEN.
Wild, H. Ueber die Differ enz der mit einem Unifilar-Theodolith und
einem Bifilar-Theodolith bestimmten Horizontal- Intensitaten des
Erdmagnetismus. Bull. Acad. Imp. Sciences. St. Petersbourg. 1898,
April. T. VIII. No. 4.
In dieser Arbeit zeigt der Verfasser, dass eine Differeuz in den Werthen
der Horizontalcomponente des Erdmagnetismus, welche er mit den genannten
und von ihm friiher beschriebenen beiden Instrumenten erhalten hat, we-
sentlich reducirt wird durch Anbringung von Correctionen, die bisher bei den
Beobachtungen gewohnlich vernachlassigt worden sind. Wahrend namlich
die Sicherheit der Beobachtung in jedem Falle eine sehr befriedigende ist,
hat doch die DifFerenz der beiden Instrumente eine ca. zehn mal grossere Un-
sicherheit.
Von den genannten Correctionen sind hervorzuheben, beim Bifilar-Theo-
dolith. bei welchem gewissermassen eine Wagung stattfindet, eine Reduction
der Masse auf den luftleeren Raum, also eine hydrostatische Correction ; bei
dem Unifilar-Theodolith dagegen ist eine Correction fiir den Einfluss der
Luft auf die Schwingungsbeobachtungen, also eine hydrodynamische nahe-
rungsweise bestimmt. Beim Bifilar-Theodolith steckt ausserdem eine Feh-
lerquelle in der Beriicksichtigung der Elasticitat der Aufhangefaden ; am
Unifilar-Theodolith endlich wird als wesentlich die Querinduction des Erd-
magnetismus und die gegenseitige Induction der Magnete aufeinander in
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144 RECENT PUBLICATIONS [vol. iv, no. 2.)
Rechnung gezogen. Im Endresultat ergiebt sich, dass durch alle diese
Correclionen die Differenz der beiden Instrumente auf etwa die Halfte redu-
cirt wird. Sie bleibt alsdann mit 0.00009 C. G. S. immer noch betrachtlich,
doch geht aus der Abhandlung zur Geniige hervor, wie wichtig fur die Zu-
kunft die Beriicksichtigung jener Correctionen sein wird, wenn man ein-
wandfreie Werthe erzielen will. Vor allem aber tritt der Nutzen hervor, der
durch die Anwendung verse hiedenat tiger Instrumente zur Messung dessel-
ben Bestimmungsstiicks erreicht wird. Hierdurch allein wird man erst auf
ganz versteckte Fehlerquellen aufmerksam.
Vielleicht ist diese Besprechung eine geeignete Stelle, um die Nothwen-
digkeit eines neuen voll standi gen, Theorie und Praxis der erdmagnetischen
Messungen zusamnienfassenden, Lehrbuchs des Erdmagnetismus hervorzu-
heben.
Die Theorie der erdmagnetischen Mess instrumente verdankt dem Ver-
fasser eine gauze Reihe von Ausarbeitungen, die ihren vollen Werth aber erst
durch Aufnahme in ein Lehrbuch erhalten. Die, wie wir horen, im nachsten
Jahre bevorstehende Herausgabe eines vollstandigen Handbuches des Erd-
netismus in der Ratzerschen Bibliothek geographischer Handbiicher wird
jedenfalls nicht nur von den Fachgenossen sondern auch von weiteren Krei-
sen freudig begrusst werden.
M. KSCHENHAGEN.
RECENT PUBLICATIONS
Da vies, J. E. Terrestrial Magnetism and the Deviations of the Compasses of
Iron Ships. Repr. from the Wisconsin Engineer, May, 1899. Pp. 243-262.
17 x 26 cm.
[An excellent resume" of the main facts of the earth's magnetism.]
Folgheraiter, G. Sulla Perturbazione magnetica del 9 settembre (1898).
Estratto dall' Elettricista" anno VII. Novembre 1, 1898, Roma. Pp. 2.
19 x 27 cm.
Richerche sulla variazione secolare dell' inclinazione mag-
netica tra il VII secolo A. Cr. ed il i secolo dell' era volgare. Note.
Roma, 1899. 19 x 28 cm.
Lagrange, E. Perturbation magne'tique du 9-10 Septembre, 1898. Bull, de
la Societe Beige d'Astr. Mars, 1899.
Lenz. Ergebnisse der magnetischen Beobachtungen in Bochum im Jahre
1898. Sonderabdr. aus Berg und Huttenm. Wochschr., No. 7, '99. Essen,
1899. Pp. 14. One plate. 22 x 29 cm.
LiTTLEHALES, G. W. The secular change in the direction of [the lines of
force] of the terrestrial magnetic field at the earth's surface. Phil. Soc.
of Washington. Bull., Vol. XIII, pp. 269-336, pis. 13-19 and folder.
15x23 cm.
[The author gives here in a collected form the data and the results of his
valuable secular variation investigations. Cf. Vol. Ill, p. 193.]
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[Plate V]
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Terrestrial Magnetism
and
Atmospheric Electricity
volume iv SEPTEMBER, 1899 number 3
L,E CADET'S TREATISE ON ATMOSPHERIC ELECTRICITY. 1
Reviewed by Alexander McAdie.
Dr. Le Cadet has given in this volume of 200 pages a very general
review of our knowledge of atmospheric electricity. Specifically, the
chief aim of the work is to critically review present theories as to the
origin of the electricity of the atmosphere in the light of certain modern
determinations of the strength of the earth's electric field. Many years
ago Sir William Thomson desired that we might have a general electrical
survey, showing the surface density of the electrical charge on the earth's
surface. If this were known, we could determine the normal values of
the earth's field. It would also be shown whether masses of electrified
air were the chief factors controlling the earth charge, and also what the
upper limit of the air electrification might be. It is almost impossible
to determine proper reduction coefficients for various points on the
earth's surface, and so, lines of equal electrical potential are unknown.
It is also evident that the relations existing between the potential and
the various meteorological elements can only be imperfectly established
by observation at the earth's surface. The study of the electricity of the
air is restricted, as in Meteorology, by our inability to undertake work in
the free air at a sufficient elevation, identical with that done at the
surface. In common, then, with most workers of to-day, Dr. I<e Cadet
recognizes the necessity of reaching out from earth and studying the
electrification of the air in situ. In brief, the purpose of this memoir is
to direct attention to what may be called modern exploration of the
earth's electrical field.
1 Etude du Champ Electrique de V Atmosphere, par Georges Le Cadet. An-
nates de V University de Lyon. Paris. Librairie J. B. Bailliere et Fils.
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I4> 6 A. MCADIE [vol. iv, No. 3.)
In the chapter devoted to instruments, there is given a full exposition
of the errors peculiar to collectors as well as electrometers, and the chap-
ter has evidently been written by one who is very familiar with the
different types of instruments. Water-droppers, flame collectors, burn-
ing matches, and mechanical devices are discussed, and that the author's
reading has been extensive is shown by references to devices not known
except to those who are specially interested in this line of investigation.
It is an open question whether our present instrumental equipments
should not be regarded as provisional. Plates and points which lose
their electrification upon exposure to certain solar rays may lead to col-
lectors giving fixed values; but at present, it must be confessed, the
experimenter is far from feeling confident that the values obtained by
him in any piece of experimental work have not been vitiated by instru-
mental errors which he is powerless to eliminate. A small flame of
illuminating gas is perhaps the handiest collector, since it takes but a
few seconds to impart to the surrounding metal and needle the potential
of the air. Morrill's flame collector is accorded high praise by Dr. Le
Cadet, as it indeed deserves.
The portable apparatus used by Exner, and the different devices of
Elster and Geitel, are discussed. A small metallic lamp, supported by an
ebonite rod inclosed in a glass tube, makes a serviceable collector. In
discussing the different forms of water collectors, attention is called to
the methods employed by S. A. Andree at Cap Thordsen, Spitzenberg, in
1882-3, for use during low temperatures. Perhaps the collector of Row-
land and Morrill — the so-called mechanical collector — will yield the most
constant results.
The chapters dealing with the exploration of the atmosphere are full
of detailed information. The two fundamental laws as given by Peltier
are: 1st. That in clear weather the potential over conducting surfaces
increases in general with elevation ; 2d. If we consider only the rate of
increase of potential with regard to height, this increase d V/dN % rep-
resenting the intensity of the field, will vary, barring surface irregulari-
ties, proportionately with the density of a negative charge distributed
over the earth surface, conformably to the equations of electrostatic
equilibrium.
The chapters devoted to detailed accounts of the different attempts
by means of balloons to measure the potential gradients, constitute a
valuable contribution to our knowledge of this subject, and will prove
very serviceable to future experimenters.
McAdie's experiments at Blue Hill with kites and electrometers, in
1 89 1, are referred to as illustrating one of the few possible ways of ob-
taining accurate measurements of the potential . gradient. Exner's
experiments with small balloons carrying a match collector and fine
copper wires are given at some length ; and also the experiments of
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LE CADET'S ATMOSPHERIC ELECTRICITY 147
Lemstrom, Semmola at Naples with captive balloons, Holmgrem, Ch.
Andre\ and Le Cadet. In the first ascension of the last named, made on
September 27, 1892, two of the party of three were injured in the rapid
descent, due to a storm. On September 15, 1892, Dr. Josef Tuma
obtained the following values from 10 A. M. to 3 P. M ;
Height in meters
410
500
750
820 1000 1 1 20
1300 1900
Potential fall in volts per meter
40
44
47
52 53 55
60 70
On August 1 and August 9,
, 1893, Dr. Le
: Cadet made
some very
successful ascensions,
the results of which in
brief were :
Mean height Fall of Poten-
Mean height
Pall of Poten-
above ground tial
l per meter.
above ground
tial per meter
August i. 615 meters
75 volts
August 9. 824 meters
37 volts
740
45
830
43
790
35
1060
43
870
26
"55
41
1005
29
1290
42
1 100
27
1745
34'
1 150
38
1940
25
1300
33
2080
2I20
2310
2520
21
19
18
16
The somewhat remarkable result appears from these observations,
that during clear weather the field does not strengthen with alti-
tude. Bornstein's observations in the balloon Phcenix, August 18 and
September 29, 1893, also show a decrease in the potential gradient with
elevation. Baschin's determinations, February 17, 1894, also confirm
the above. In brief, it would seem that in middle latitudes, as a rule,
the electricity of the air is positive, but that in the lower strata, up to
2,000 meters, the positive masses are offset by negative masses, some-
times feeble, sometimes strong ; and the positive electricity predominat-
ing above is about neutralized at 5,000 meters by the negative charge
of the earth and the lower layers of atmosphere.
On March 24, 1897, with new apparatus, a third ascension was made
by Le Cadet, with the following results:
Altitude
dN
dV
dN/dV
(meters)
(meters)
(volts)
1680
5
140
28
1700
5
158
32
1780
5
149
30
1810
5
155
31
1850
5
158
32
1880
5
145
29
1900
5
149
30
2200
5
149
30
2300
5
145
29
At the Observatory at Lyons* the potential as registered on the elec-
trometer gave a mean value for the field of 99 volts per meter for an
altitude of 300 meters. The first deduction then is that the field was less
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148 <*- MCA DIE [vol. iv, no. 3]
strong at 1,500 meters in the free air than near the ground. It is note-
worthy that approximately the same value was obtained by all experi-
menters at an elevation of 1,800 meters.
The fourth ascension was made on September 11, 1897, and we shall
give but a few of the many values then obtained :
Altitude
dN
dV
(meter*)
(meters)
(volts)
dN/dV
1 1 20
5
220
44
1050
5
210
42
1 120
5
220
44
II50
5
210
42
1260
5
206
41
1300
5.
197
39
I370
5
188
38
1400
5
180
36
I550
5
201
40
1700
5
139
28
1800
5
133
27
2IOO
5
112
22
2200
5
no
22
2500
5
112
22
3000
5
95
19
4000
10
134
13
4I50
10
112
n
3900
10
I48
15
Taking the mean of 26 observations made when the balloon was fairly
constant at an elevation of 4,000 meters we have d V/dN—i$o±20 vm.
Following Exner, the relation between the distribution of the water
vapor and the electrification of the air is discussed at length.
Le Cadet advances a new view concerning the origin of the positively
electrified masses of the atmosphere. He holds that the field is the
result of the negative electrification of the earth surface and the equiva-
lent positive electrification of the free carbon dioxide. Carbon dioxide
being a constituent of the atmosphere, the general distribution would
conform to the general pressure distribution. Both the production and
absorption of carbon dioxide occur at the earth surface, and it is in the
lowest levels that we find the most marked variations.
Excellent curves showing the perturbations recorded during dust
storms and the apparent relationship between the dustiness of the atmos-
phere and its electrification are given from the records of the Observa-
tory at I,yons.
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SUR LA PERIODICITE DES PERTURBATIONS DE V AI-
GUILLE AIMANTEE HORIZONTALS A L'OBSER-
VATOIRE DU PARC SAINT-MAUR.
Par M. Th. Moureaux.
La s£rie des observations magn&iques faites k Tobservatoire du
Pare Saint-Maur remonte au i er Janvier 1883; elle comprend done
actuellement seize ann£es. Les courbes de variations de D, H et Z
sont r&iuites, et transferases en tableaux qui donnent, pour chaque
heure, la valeur absolue de ces trois £16ments. Le r£sum6 des
quinze premieres ann6es, qui vient d'etre public, permet ainsi la
discussion de 131,496 observations.
Nous n'envisagerons ici que la variation horaire et mensuelle
des perturbations de la d&linaison et de la composante horizontale.
Ce mot perturbation doit d'ailleurs s'entendre au sens le plus large ;
il ne s'aplique pas seulement aux grands orages magn&iques ; mais
k toute valeur horaire s'6cartant de sa valeur normale, dans un sens
ou dans Pautre, d'une quantity d£termin6e.
Pour la d^clinaison, par exemple, on a consid£r£ comme pertur-
bation toute valeur de cet 6l6ment diff&rant au moins de 3' de la
moyenne horaire mensuelle correspondante ; de m£me, les valeurs
de la composante horizontale diffSrant de 0.00020 de la moyenne
horaire mensuelle ont iti consid£r6es comme perturbations. Dans
chaque cas, on a distingu£ le sens des irr£gularit£s observes. Ces
departs sont £videmment arbitraires, mais il ne semble pas que le
choix d'une autre limite soit de nature k modifier la distribution
relative des valeurs troubles, soit dans le cours de la journ£e, soit
dans le cours de l'ann£e.
Sur les 131,496 valeurs horaires de la s£rie, on en compte,
comme troubles ainsi qu'il vient d'etre dit, 8767 pour la declinai-
son et 14730 pour la composante horizontale, soit respectivement
7 et 11 %. Ces perturbations se r^partissent comme suit, selon les
ann6es :
1883
1884
1885
1886
1887
1888
1889
1890
1891
1892
1893
1894
1895
1896
1897
TOTAUX
D
H
606
II42 1
527
917
564
1058
765
1030
465
659
400
527
340
403
270
314
547
943
949
1851
648
1 199
815
1556
749
1222
651
1258
47i
671
8767
14730
1
Les mo
is d'a
vril €
>t ma
i ne s
ont p
as co
mpri
MS
3 dan
\
s ce t
otal.
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150 TH. MOUREAUX [vol. iv, no. 3.]
Le minimum annuel du nombre des perturbations se trouve en
1889-90 et coincide sensiblement avec celui de l'activit£ solaire.
Les maxima des taches de part et d'autre de ce minimum, se sont
produits en 1883 et en 1893. Le premier maximum des perturba-
tions est trfes net en 1883; le second se reporterait plutdt sur les
ann£es 1892 et 1894, de part et d'autre de 1893.
Deux diagrammes (page 151) accompagnent cette note. Le
premier montre la distribution horaire, et le second la distribution
mensuelle des perturbations. Dans le premier, le premier groupe
de trois courbes est relatif k la d£clinaison, et le second, k la com-
posante horizontale ; la courbe pointill£e repr^sente, dans les deux
cas, les perturbations dans le sens d'une augmentation de lament
consid&*6, la courbe en traits discontinus figure les perturbations
dans le sens d'une diminution, enfin la courbe pleine reprdsente le
total des perturbations, abstraction faite de leur signe.
En ce qui concerne la declinaison, on voit que les troubles ay ant
pour effet de diminuer cet £16ment, en rejetant vers Test le pdle
nord de l'aimant, sont peu fr^quentes pendant le jour, avec un mini-
mum vers 7 h du matin; k partir de 4 h du soir, le nombre des pertur-
bations de cet ordre augmente rapidement, et passe par un maxi-
mum trfes €\ev€ vers le milieu de la nuit. Au contraire, les pertur-
bations dans le sens d'une augmentation sont relativement rares
pendant la nuit, et pr6sentent un maximum vers i h du soir.
Les courbes diurnes des perturbations de la composante horizon-
tale ont une allure toute diffSrente. Dans le cours de la journ£e, les
perturbations qui diminuent la composante sont constamment plus
fr^quentes que celles qui Taugmentent ; les deux courbes sont sen-
siblement paralteles de n h du soir k io h du matin, et le minimum
de troubles, pour Tune et Tautre s£rie, se produit k 4 h -5 h du matin.
Le maximum des perturbations qui augmentent Jfse produit k io h
du matin; pour celles qui diminuent cet 616ment, la courbe con-
tinue de monter et le maximum n'est atteint qu* k 2 h du soir. Les
hearts entre les nombres horaires qui repr^sentent chaque sorte de
perturbations atteignent leur plus grande valeur le soir, entre midi
et 9 h .
Le diagramme 2 repr&ente la repartition des perturbations de
la declinaison dans le cours de Tannic Les totaux mensuels met-
tent en Evidence une double oscillation annuelle, avec deux minima
aux solstices et deux maxima aux Equinoxes, le maximum principal
correspondant k l'6quinoxe d'automne et le minimum principal au
solstice d'hiver. Les chiffres relatifs a la composante horizontale
conduiraient k la construction d'une courbe de mgme forme, et cette
distribution persiste, soit que Ton considfere Tensemble des pertur-
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P&RIODICIT& DES PERTURBATIONS
151
bations, soit qu'on les groupe suivant le sens dans lequel elles se
prodtiisent.
D'une manure g£n£rale, les perturbations qui diminuent D et//
sont dominantes ; toutefois, en juillet et aotit pour D, en aotit seul-
<
» I
r <
1* » v midi 3* \
V 9- mn
.100
/
40O
DECLtt
'A/JU/V
300
\
\
>
total ^
/ ,'''
/
200
\
>
.feitive*
y
*•
/
/
/
too
,.*"*
.....v*
v.
■•'*
Negatives
V
• •
\
v.^.
•••.
..••
600
700
lofal
000
COt
KflOSM*
vjftm
ra/i
500
400
/
*>
^Negatives
300
^y
1
/ ,•
/
*'*--
-..
700
i ^^ ^
•
— ^y
y /
.
Positive*
^
l
» J F M A M J «
\ A §
\ 1
i D
000
6/S,
W J?/S
yr/a
V Ml
'MSV.
flit
Aoo
roo
1
s
\
600
\
600
1
Variation diurne et annuelle des perturbatious de l'aiguille aimantee
horizontale, a l'Observatoire du Pare Saint-Maur. (1883— 1897.)
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1 5 2 TH. MO UREA UX [Vol. iv, No. 3. j
ement pour ff, les perturbations en sens inverse sont les plus fr6-
quentes.
Les observations relatives k la composante verticale n'ont 6t6
trait6es k ce point de vue qu' k partir de 1889. Les conclusions
tiroes de la discussion des neuf ann6es de 1889 k 1897 conduiraient
k des r6sultats identiques, quant k la distribution g6n6rale des per-
turbations ; on remarquerait toutefois que les troubles de H et de Z
6tant le plus souvent de sens oppos6, les perturbations positives de
ce dernier 6l6ment sont plus fr6quentes que les perturbations neg-
atives.
Les perturbations des 616ments magn6tiques, telles que nous les
avons envisages ici, suivent done une loi diurne, absolument
comme les variations r6guli£res. L'inegalite diurne de chacun des
616ments diff6rera n6cessairement, suivant qu'elle sera calcul6e
d'apr&s Tensemble des observations horaires, ou qu'on utilisera settl-
ement les jours de calme magn6tique. Au Pare Saint-Maux, par
exemple, les variations irr6gulieres ont pour effet, en toutes saisons,
d'augmenter la declinaison pendant le jour et de la diminuer pen-
dant la nuit. Cette influence est plus marquee en hiver qu'en 6t6,
en sorte que, pendant les mois d'hiver, alors que la variation r6g-
uli&re est faible, le minimum de nuit devient constamment le mini-
mum principal. L'accentuation de ce minimum doit £tre attribute
k Taction des perturbations negatives ; en effet, il reste secondaire
si rin6galit6 diurne est calul6e d'apr&s les jours calmes settlement.
La variation diurne d'un 616ment magn6tique, d6duite de Ten-
semble des observations horaires, n'est done en r6alit6 que la r&ult-
ante de deux ph6nom£nes au moins, se superposant. L'un est la
variation solaire proprement dite, telle quelle r6sulte des seules
observations correspondant k une situation magn&ique normale,
Tautre est la variation due aux perturbations, dont la p6riode est
6galement d'un jour solaire, mais dont Tamplitude et les phases
sont variables, selon les positions g6ographiques.
II est done 6galement important que l'in6galit£ diurne des 616-
ments soit calcuI6e par les deux m6thodes. La question faisait d'ail-
leurs partie du programme soumis k la premiere Conference mag-
netique internationale, dans sa reunion de Bristol, en septembre
dernier, et on sait que le Comit6 permanent a adopt6 la resolution
suivante: " Dans le calcul des moyennes mensuelles, tous les jours
doivent fetre pris en consideration. II est desirable de publier en
outre les moyennes calcul6es sans tenir compte des jours de per-
turbations."
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UBER DIE MOGUCHKEIT, VOLLSTANDIGE MAGNETI- ./
SCHE OBSERVATORIEN GANZ OBERIRDISCH UND v
IN EINEM GEBAUDE EINZURICHTEN.
Von H. Whd.
Herr Professor M. Eschenhagen bat in Nr. i des IV. Bandes
dieter Zeitschrift meinen Plan fur Einrichtung magnetischer Ob-
scrvatorien 1 in einer Weise besprochen, welche meines Erachtens
iiber den Zweck und die Bedeutung meines Vorschlags zu irrigen
Meinungen fuhren konnte. Es sei mir daber gestattet, bier im In-
teresse der Sacbe einige rectificirende Bemerkungen zu dieser kriti-
schen Besprechung zu machen und die in Betracht kommenden
Fragen etwas eingehender zu erortern.
Herr Eschenhagen mocbte meinen Plan, der die Vereinigung
der absoluten erdmagnetischen Messungen und der Variations-
Beobacbtungen in einem oberirdischen Gebaude vorschlagt, nur fur
solche Falle adoptiren, wo es aus okonomischen Riicksichten nicht
moglicb sei, mebrere Gebaude zu erricbten. Da es ihm wichtig er-
scbeint, sowohl fur die absoluten Messungen als fur die Variations-
Beobacbtungen je zwei Serien verschiedener Instrumente in einem
vollstandigen magnetischen Observatorium zu haben, so bait er es
fur besser, wie bisher zwei getrennte Gebaude zu erstellen, das eine,
oberirdische, fur die beiden Serien der Instrumente zu den absolu-
ten Messungen, und das andere, unterirdische, fur die zwei Serien
von Variationsinstrumenten, wie dies kiirzlich in Potsdam einge-
ricbtet worden sei, nachdem sich dort die seit 1890 bestehende
Vereinigung der absoluten Messungen und der Variations-Beobach-
tungen in einem Gebaude, namlich die letztern im Keller und die
ersteru im Erdgescboss dariiber, nicht bewabrt babe. Ausserdem
solle noch ein drittes Gebaude fur besondere Untersuchungen in
grosserer Entfernung von den erstern daselbst erstellt werden.
Diese von Herrn Eschenhagen befurwortete und gegenwartig
in Potsdam adoptierte Modification der bisberigen Einrichtung ent.
spricht nun aber im Princip d. h. abgesehen von gewissen Details
ganz der von mir seiner Zeit in Pawlowsk getroffenen und seit 1878
in ununterbrochener Function begriffenen Anordnung und Ver-
tbeilung der magnetischen Beobacbtungen. Das unterirdische Ge-
> Bulletin de VAcad. Imp. des sciences de St. Petersbourg. \t s6rit, T. VIII.
N. 3 (1897).
2 153
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154
H. WILD [Vol. IV, No. 3.)
baude fur Variations-Beobachtungen — eigentlich ist dasselbe ober-
irdisch angelegt, verhalt sich aber wie ein unterirdisches, da es mit
doppelten Gewolben und Wanden versehen und mit eitier dicken,
einen Hiigel bildenden Erdschicht bedeckt ist — besteht aus zwei
durch einen Corridor getrennten Salen, von denen der eine den
Magnetographen englischen Systems und der andere die Varia-
tionsapparate fiir directe Beobachtung und ausserdem noch die zwei
selbstregistrirenden Erdstrom-Galvanometer enthalt. Der ganz
eisenfreie Pavilion fur absolute Messungen umfasste anfanglich
zwei durch Doppelthiiren getrennte Raume, namlich einen grossen,
heizbaren kreuzfbrmigen Saal fur zwei Serien von Instrumenten zu
absoluten Messungen und einen nicht heizbaren kleineren Raum
fiir astronomische und Declinations-Beobachtungen, zu welchen
seit 1883 durch einen ebenfalls eisenfreien Anbau noch ein drittes
' Zimmer zur besseren Trennung der zweierlei absoluten Messungen
hinzugekommen ist. Ausser diesen zwei grosseren Gebauden sind
aber noch ein kleineres heizbares Gebaude fiir eine dritte Serie von
Variations-Apparaten und zwei eisenfreie nicht heizbare Holzhiit-
ten fiir absolute Messungen von Lernenden, fiir Vergleichung frem-
der Instrumente mit den Normal-Instrumenten der Anstalt und fiir
Untersuchung neuer Apparate vorhanden. Dieses Observatorium
ist von mir summarisch im Bulletin der Kaiserl. Academie der
Wissenschaften zu St. Petersburg, T. XXV., p. 17-51 (1878) be-
schrieben worden und wenig spater wurden auch der Konigl. Preus-
sischen Regierung auf ihren Wunsch detaillirte Plane desselben
officiell zugestellt. Eine ausfiihrliche Beschreibung des Observa-
toriums mit Ansichten und Planen sowie einer eingehenden Eror-
terung iiber die Sicherheit der darin ausgefiihrten Beobachtungen
ist in meiner 1895 von^der Petersburger Academie herausgegebe-
nen Schrift : "Das Konstantinow'sche meteorologische und magne-
tische Observatorium in Pawlowsk" enthalten. Auch Herr C. C.
Marsh macht in seinem Bericht 1 iiber die von ihm im Jahre 1889
im Auftrage des Marine-Secretars besuchten magnetischen Obser-
vatorien in Europa verschiedene Mittheilungen iiber diese Anstalt
und sagt von ihr: "The nearest approach to perfection yet attained
is the Russian Observatory at Pawlowsk near St. Petersburg. Here
has grown up the most complete magnetic establishment of the
world."
1 C. C. Marsh, Ensign U. S. Navy, A Report upon some of the Magnetic Obser-
vatories 0/ Europe. Washington 1891. Appendix I to Washington Observations,
1887.
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VOLLSTANDIGE MAGNETISCHE OBSERVATORIEN
155
Trotz dieser von unparteiischer Seite als so vollkommen ge-
riihmten magnetischen Einrichtungen in Pawlowsk haben gerade
die langjahrigen Erfahrungen an denselben es mir rathlich erschei-
nen lassen, in gewissen Theilen fur zukiinftige Begriiudungen mag-
netischer Observatorien Modificationen vorzuschlagen und zwar
nicht, wie es Heir Escbenhagen zu glauben scheint, aus okonomi-
scben Griinden, sondern im Interesse der Genauigkeit der Beobach-
tungen und der Bequemlichkeit der Beobachter, was ja unzweifel-
haft zur Erhohung der erstern auch beitragt.
Zunachst erschien es mir hochst wiinschenswerth, die Instru-
mente fur die absoluten Messungen in ihrem Local so zu disponie-
ren, dass sammtliche Magnete bestandig in diesem verbleiben kon-
nen, ohne gegenseitige Storungen befiirchten zu miissen, und dass
so, wie icb es in der erwahnten Abhandlung ausdriicklich angege-
ben habe, der lastige und die Sicherheit der Messungen gefahr-
dende Transport der Magnete in audere, mehr oder minder, ent-
fernte Localitaten vermieden werden konne, folglich auch die frag-
lichen Instrumente zu jeder Zeit zur Ausfuhrung der absoluten
Messungen unmittelbar bereit seien.
Da ferner die photographischen Aufzeicbnungen des Magneto-
graphs bei aller Vorsicht doch hie und da Unterbrechungen sei es
durch das Stillstehen der Uhrwerks, sei es durch Ausgehen des
Lichts, sei es durch Fehler im lichtempfindlichen Papier ausgesetzt
sind, so erschien es schon aus diesem Grunde, abgesehen von der
Erlangung grosserer Genauigkeit, geboten, zur Zeit der absoluten
Messungen die betreffenden zweiten Variations-Instrumente im an-
dern Saal des unterirdischen Gebaudes direct beobachten zu lassen.
Der Umstand indessen, dass man zu dem Ende stets einer zweiten
Person bedurfte, wurde mir und Anderen haufig unbequem und
storend, obschon kein Personen-Mangel in Pawlowsk stattfand.
Dazu kam aber noch, dass man sich mit dieser Person im unter-
irdischen Gebaude iiber die Zeitpunkte der zu machenden simul-
tanen Ablesungen Seitens des Beobachters im Pavilion fur absolute
Messungen nur durch electrische Glocken-Signale verstandigen
konnte, was nicht selten zu Missverstandnissen und damit zum
Verlust von ganzen Beobachtungsreihen Veranlassung gab. Hier-
aus entstand der zweite Wunsch, wenigstens die Variations-Instru-
mente fiir directe Beobachtung in solcher Nahe bei denen fur abso-
lute Messungen zu haben, dass der Beobachter an den letzteren
eventuell auch die ersteren selbst ablesen oder dann wenigstens
den Beobachter derselben unter Augen haben und sich unmittel-
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156 H. WILD [vol. iv, No. 3.
bar mit ihm verstandigen konnte. Wenn es aber moglich sein
sollte, zu dem Ende in demselben Gebaude die Instrumente fur
absolute Messungen und diejenigen fur directe Variations-Beobach-
tungen unterzubringen ohne gegenseitige Storungen derselben zu
riskiren, so musste es angehen, den Magnetographen ebenfalls im
gleichen Gebaude ohne Schaden aufzustellen und so Alles beisam-
men zu haben.
Diesen Erfahrungen und Erwagungen gemass entstand der be-
sprochene Plan eines Gebaudes, in welchem eine Serie von Instru-
menten fur absolute Messungen und die beiderlei Variations-Instru-
mente ohne Risiko einer gegenseitigen Stoning, trotz dem steten
Verbleib der Magnete der ersteren im Local, unterzubringen waren.
Dass der letztere Zweck vollkommen durch meinen Plan 1 erreicht
sei, gibt Herr Eschenhagen in seiner Besprechung zu.
Dagegen fiirchtet Herr Eschenhagen von der Anstellung der
absoluten Messungen und der dazu gehorenden directen Variations-
Beobachtungen durch dieselbe Person erstlich eine Vergrosse-
rung der Zeitdauer einer completen Beobachtung und zweitens
eine Verminderung der Genauigkeit wegen nicht geniigender
Gleichzeitigkeit der beiderlei Beobachtungen. Den ersteren Ein-
wand muss ich als einen praktisch ganz hinfalligen bezeichnen,
denn die Zeit, welche der Beobachter braucht, um einen, hochstens
zwei Variations- Apparate abzulesen, ist neben der, welche er jewei-
len fur die mannigfachen Manipulationen, Einstellungen und Ab*
lesungen an den absoluten Messinstrumenten benothigt, eine so
minime, dass sie daneben gar nicht ernstlich in Betracht kommen
kann. Wenn man dagegen nicht, wie dies, wenigstens zu meiner
Zeit, in Pawlowsk geschah, durch electrische Glockensignale den
Beobachter im fernen Variationsgebaude zur Ablesung der Varia-
tions-Instrumente auffordert, sondern, wie dies in Potsdam ge-
schieht, zuerst mittelst Stromesschluss im Pavilion fur absolute
Messungen eine electrische Lampe vor seinen Augen im Variations-
gebaude aufleuchten lasst und nach derartiger Erregung seiner
Aufmerksamkeit ihn befahigt, genau im Moment des Erloschens
derselben, was das eigentliche Signal fur die Ablesung an den
Variations-Instrumenten darstellt, diese zu machen, so wird eine
solche Ablesung mit der definitiven Einstellung auf die Magnete
an den absoluten Instrumenten allerdings simultaner erfolgen kon-
1 Es sei hier bemerkt, dass ich inzwischen bei Gelegenheit eines Entwurfs for
ein magrnetisches Observatoritim in der Schweiz noch zu einer anderen Losung die-
ses Problems gelangt bin, welches gegeniiber dem ersteren erhebliche Vortheile
darbietet. [Cf. p. 169.]
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VOLLSTANDIGE MAGNETISCHE OBSERVATORIEN 157
nen, als wenn der Beobachter an den letzteren noch einige Schritte
nach den Variations-Instrumenten hin behufs ihrer Ablesung zu
machen hat. Da man indessen im Falle von Storungen resp. ra-
schern Bewegungen der Magnete, abgeseben von Beobachtungen
in Polargegenden, iiberhaupt keine absoluten Messungen anzustel-
len pflegt, so durfte eine Verspatung von einigen Secunden im
Ablesen der Variometer kaum von praktischer Bedeutung fur die
Reduction der ersteren sein. In Pawlowsk sind haufig zu dieser
Reduction nicht bloss die simultanen directen Ablesungen an den
Variometern, sondern auch die Aufzeichnungen des Magnetogra-
phen benutzt worden, bei welchen die Zeit hochstens auf 20 Se-
cunden genau zu schatzen war (1 Stunde = 15 mm. der Zeit-
Abscissen der Curve), und doch ergab sich dabei durchweg in den
beiderlei Reductions-Resultaten kein merklicher Unterscbied. Wenn
aber Herr Eschenhagen sagt, dass der Mangel an Gleichzeitigkeit
besonders bei den Schwingungsbeobachtungen fiihlbar sein werde,
so trifft dies wenigstens bei der in Pawlowsk hiebei befolgten Beo-
bachtungsmethode nicht zu. Da man namlich dort zunachst wah-
rend 100 Schwingungen die Zeiten jedes 5. Durchgangs des Mag-
nets durch die Gleichgewichtslage notirte, dann eine grossere ge-
rade Zahl von Schwingungen (je nach Bediirfniss 100 bis 200
Schwingungen) unbenutzt voriiber gehen Hess und darauf analog
wieder wahrend 100 Schwingungen jeden 5. Durchgang beobach-
tete, 1 so ware offenbar durch Ablesungen am Bifilarmagnetometer
vor Beginn und nach Schluss dieser Beobachtungen sowie beliebig
oft in dem fraglichen Intervall von 100 bis 200 Schwingungen die
Gleichzeitigkeit hinlanglich zu wahren gewesen. Fur besonders
genaue Beobachtungen ist es iibrigens auch bei unserer Anordnung
der Instrumente nicht ausgeschlossen, durch einen zweiten Beobach-
ter die Variations-Apparate ablesen zu lassen, wobei, wie schon
oben bemerkt, die unmittelbare Verstandigung mit ihm und eine
Controle Seitens des Beobachters an den absoluten Instrumenten
gegenuber der Vertheilung in zwei Gebauden nur von Nutzen sein
kann.
Fur den Fall, dass kein zweiter Beobachter zur Hand sei, wiirde
es Herr Eschenhagen fur besser erachten, nach der photographi-
schen Registrirmethode von K. Schering und C. Zeissig* im zwei-
ten fernen Gebaude der Variations-Instrumente den augenblick-
1 Siehe z. B. meine Abhandlung: Neuer ma%netischer Uniftlar-Theodolilh, S.
24 und 25. M£m. de l'Acad. Imp. de9 sciences de St. Petersbourg. VII # . s^rie, T.
XXXVI., N. 1 (1887).
* Wiedemann's Annalen, Bd. 53, S. 1039 (1894).
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158 H. WILD [Vol. iv, No. 3.]
lichen Stand dieser durch electrische Uebertragung photographiren
zu lassen. Die Methode dieser Herren ist gewiss sehr sinnreich
und wiirde sich auch wohl zu vorstehendem Zwecke benutzen las-
sen, meines Wissens ist aber bisher durch keine vergleichende
Versuchsreihe mit gleichzeitigen directen Beobachtungen nachge-
wiesen worden, inwiefern der beziigliche Apparat langere Zeit
sicher und genau functionirt; die der Beschreibung beigefiigten
Resultate zeigen nur, dass man mittelst desselben Aufzeichnungen
von Magnetometer-Scalenstanden und den zugehorenden Zeiten
erhalten kann. Ehe die Autoren selbst jenen Nachweiss leisten,
wird sich daher kaum Jemand dazu verstehen, den nicht ganz ein-
fachen Apparat in einem magnetischen Observatorium einzufuh-
ren. Da iibrigens der Scalen- resp. Magnet-Stand auch hier durch
die Photographie fixirt wird, so unterliegt dies Verfahren ganz
denselben, oben gemachten Einwanden gegen den gewohnlichen
Magnetograph, welche eben die sichere directe Beobachtung an
einer zweiten Serie von Variations-Instrumenten wiinschenswerth
erscheinen liess. Die grossere Genauigkeit aber beziiglich der
Zeitangabe kann auch bei den bereits ausprobierten Magnetogra-
phen nach Herrn Eschenhagen's Vorschlag durch eine raschere
Drehung und passende Vergrosserung der Trommeln mit dem
empfindlichen Papier erzielt werden. Dass aber weiterhin Herr
Eschenhagen die Registrirmethode von Schering und Zeissig spe-
ciell fur Polarstationen glaubt empfehlen zu miissen, weil dort we-
gen der Feuchtigkeit das Bromsilber-Gelatine-Papier fur die Regi-
strirung nicht geeignet sei, ist mir geradezu unverstaridlich, da ja
bei jener Registrirmethode wie beim gewohnlichen Magnetograph
die Photographie benutzt wird. Sollte aber die Bemerkung des
Herrn Eschenhagen sich nur auf das Verziehen des Papiers durch
die Verschiedenheit der Feuchtigkeit desselben bei der Aufnahme
und beim Ausmessen der Curven beziehen, so hat er ja selbst in
der Einleitung zu den magnetischen Beobachtungen fur 1890 und
1 89 1 in Potsdam eine Methode angegeben, diesen Fehler zu bestim-
men. Wenn man indessen, wie dies in Pawlowsk geschieht, die
Empfindlichkeitsbestimmung der Instrumente des Magnetographs
ebenfalls durch photographische Fixirung der Ablenkungen
ausfiihrt, so wird der fragliche Fehler von selbst fast ganz
eliminirt. Endlich sei bemerkt, dass ich in der Publication der
franzosischen Polarstation von 1882-83 am Cap Horn, wo ein
Magnetograph mit Bromsilber-Gelatine-Papier die ganze Zeit tiber
functionirte und zur Ableitung aller Stundenwerthe diente, kein
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VOLLSTANDIGE MAGNETISCHE OBSERVATORIEN
159
Wort einer Klage iiber diese photographische Registrirung habe
finden konnen.
Herr Eschenhagen spricht sich ferner auch deshalb gegen mei-
nen Plan aus, weil er nicht bloss zwei verschiedene Serien von Va-
riations-Apparaten, sondern auch zwei solche von Instrumenten zu
absoluten Messungen in einem vollstandigen magnetischen Obser-
vatorium fiir nothwendig erachtet und man daher ein Gebaude fiir
alle diese Instrumente gewiss als zu klein erfinden werde. Wenn
man aber nach meinem Plan die zwei Serien von Variations-Appa-
raten und einen Satz absoluter Instrumente ohne Gefahr gegensei-
tiger Stoning in demselben Gebaude unterbringen kann, so sehe
ich nicht ein, warum durch eine passende Vergrosserung desselben
wiinschenden Falls nicht noch ein zweiter Satz absoluter Instru-
mente ebenfalls ohne Nachtheil hinzugefiigt werden konnte. Der
Gesammtumfang dieses einen Gebaudes miisste jedenfalls nicht
grosser als der zweier getrennten zusammen sein, und somit ware
durch die Vereinigung an Bequemlichkeit und auch beziiglich der
Beheizung nur gewonnen.
Es sind aber weder okonomische Rucksichten noch Schwierig-
keiten des Problems, welche mich verhindert haben, in meinem
Plane noch eine zweite Serie von Instrumenten zu absoluten Mes-
sungen aufzunehmen, sondern ich habe davon von vorne herein
wieder zufolge meiner Erfahrungen im Observatorium zu Paw-
lowsk abstrahirt. Wir disponirten daselbst iiber mehrere Instru-
mente fiir absolute Declinationsbestimmungen, iiber drei verschie-
dene Nadel-Inclinatorien, iiber vier Inductions-Inclinatorien und
fiir die absolute Bestimmung der Horizontal-Intensitat iiber zwei
verschiedene magnetische Unifilar-Theodolithen, einen magneti-
schen Bifilar-Theodolithen, zwei magnetometrische Apparate zu
Messungen nach der Gauss'schen Methode mit Spiegelablesung
durch Fernrohr und Scale und einen entsprechenden Apparat zur
Beobachtung nach der Neumann-Kohlrausch'schen Methode mit
Unifilar- und Bifilar-Magnetometer. Mit all' diesen Instrumenten
wurden im L,aufe der Zeit vergleichende absolute Messungen zum
Studium derselben gemacht, wie die Einleitungen zu den Publi-
cationen der Beobachtungen von Pawlowsk in den Annalen des
phys. Central-Observatoriums und meine beziiglichen Abhandlun-
gen in den Schriften der Academie der Wissenschaften zu St. Pe-
tersburg lehren. 1 Obschon daraus hervorgeht, dass diese verschie-
1 Bine theilwcisse Zusammenfassung dieser Resultate findet man in der oben
erwahnten Schrift: Das Konstanlinow'sche Observatorium in Pawlowsk, S.
111-121.
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160 H. WILD (vol. iv, No. 3.J
denen Instrumente jeweilen aufs genauste untersucht und die
Beobachtungen mit ihnen aufs sorgfaltigste angestellt wurden, so
zeigten sich in ihren Angaben doch Differenzen, welche die Beob-
achtungsfehler durchweg weit iiberschritten. Hie und da war es
moglich, bei der einen oder anderen Methode nachtraglich Fehler
zu ermitteln, in manchen Fallen blieben. aber die Differenzen zu-
nachst noch nicht aufgeklart. Fiir die Bearbeitung der Beobach-
tungen und Aufzeichnungen der Variations-Apparate hielten wir
uns daher stets so lange an die absoluten Messungen mit einer be-
stiramten Serie von Instrumenten, bis fur das eine oder andere
derselben durch die erfolgten Studien ein Ersatz durch ein ent-
schieden besseres Instrument geschaffen war. Niemals aber dachten
wir etwa daran, das Mittel aus den Resultaten zweier verschiede-
ner Instrumente als sicherer an Stelle des einzelnen zu setzen;
auch bin ich iiberzeugt, dass dies Herr Eschenhagen ebenfalls nicht
beabsichtigt. Die Studien an den andern Instrumenten als den
jeweilen zu den normalen absoluten Messungen benutzten, hatten
also nur den Zweck, wo moglich bessere Apparate und Methoden
zu finden und eventuell Fehler bei jenen aufzudecken. Dabei
machten wir indessen nur zu haufig die Erfahrung, dass die Ver-
einigung dieser Untersuchungen in demselben Gebaude mit den
Instrumenten fur die normalen Messungen, die jede Woche wieder-
kehrten, wegen den auf die letzteren zu nehmenden Riicksichten
fiir jene hinderlich waren. Daher entwarf ich schon im Jahre 1893
unter Benutzung der damals erfolgten Vergrosserung unseres Ter-
rains einen Plan zu einem besondern eisenfreien Pavilion behufs
separater Aufstellung der Instrumente fiir die normalen absoluten
Messungen, nach dessen, aus okonomischen Griinden nicht erfolg-
ter, Ausfiihrung dann das bisherige Gebaude eben nur fur Studien
mit andern Apparaten hatte dienen sollen.
Aus diesen Griinden habe ich in dem neuen Plan nur eine
Serie von Instrumenten fur die normalen absoluten Messungen auf-
genommen. 1st ein magnetisches Observatorium, wie dies ja leider
noch selten der Fall ist, in den Stand gesetzt, ausser den normalen
Arbeiten noch Studien an andern Instrumenten auszufiihren, so
wird es dem Obigen zutolge gewiss besser sein, wenn dafur ein be-
sonderes zweites Gebaude errichtet wird.
Dass man dagegen fiir jedes magnetische Observatorium durch-
aus zwei Serien von Variations- Instrumenten verlangen muss, ist ab-
gesehen von der gegenseitigen Controle auf Leistungsfahigkeit
und von der leichtern Bestimmung der Temperatur-Coefficienten
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VOLLSTANDIGE MAGNETISCHE OBSERVATORIEN x ^
derselben schon aus Riicksicht auf die Continuitat der Beobach-
tungen geboten. Wenn das eine oder andere Instrument versagt,
so kann dann sofort das betreffende Instrument der andern Serie in
Function treten, ja es erscheint wiinschenswerth, dass fur beide
Serien wenigstens die Moglichkeit photographischer Registrirung
vorhanden sei, damit im Falle einer grosseren Reparatur oder zeit-
gemassen Aenderung am Magnetograpb die zweite Serie von In-
strumenten zur Registrirung benutzt werden konne. Bei den In-
strumenten fur absolute Messungen hingegen wird im Intervall
zwischen den letztern fiir alliallige Reparaturen stets genug Zeit
bleiben.
Herr Eschenhagen beharrt endlich im Gegensatz zu mir dar-
auf, dass das Geb'aude fur die magnetischen Variations-Instrutnente
durchaus ein unterirdisches sein solle, da ja die Erfahrung in Pots-
dam deutlich die Moglichkeit erwiesen habe, den unterirdischen
Raum fiir die Variometer trocken und auf gleichfbrmiger Tempe-
ratur zu erhalten. Hieriiber gibt der Bericht des Herrn Directors
W. von Bezold tiber die Thatigkeit des K. preussischen meteorolo-
gischen Instituts im Jahre 1896, Abschnitt: Magnetische Arbeiten,
S. 27, folgende pracisere Aufschliisse : l "Durch den schon oben
erwahnten Anschluss an die stadtische Gasanstalt wurde die Behei-
zung des magnetischen Observatoriums noch etwas giinstiger als
frtiher, so dass jetzt die Constanz der Temperatur der unterirdi-
schen Raume, die doch standig zuganglich und ventilirt sein miis-
sen, eine ausgezeichnete ist. Die Temperatur der Raume schwankt
im Allgemeinen nur um o,°3 — o,°5 des Tags, die der Instrumente
ist noch gleichmassiger. Die Austrocknung ist nun eine so voll-
kommene geworden, dass die unterirdischen Raume mit einem
dauerhaften Anstrich von Wachsfarbe versehen werden konnten."
Also seeks Jahre hat es hiernach gedauert, bis die unterirdischen
Raume in Potsdam trocken geworden sind und bis man darin im
Laufe des Tages eine Temperatur-Constanz von o,°3— o,°5 erzielen
konnte. Eine Empfehlung zur Anlage unterirdischer Observato-
rien vermag ich entgegen Herrn Eschenhagen in diesen Daten
beim besten Willen nicht zu erkennen.
Allerdings lassen sich bei unterirdischen Gebauden durch ge-
wisse Einrichtungen auch bessere Resultate erzielen, wie die in den
Annalen des physik. Central-Observatoriums enthaltenen Einlei-
1 Seit 1892 findet man leidcr in den Ergebntssen der magnetischen Beobachtun-
gen in Potsdam weder tiber diese Verhaltnisse, noch iiber die absoluten Messungen
and die daraas abgeleiteten Normalstande der Variations-Instrumente die gering-
sten Mittheilungen.
3
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1 62 H. WILD [vol. iv, no. 3.)
tungen zu den Beobacbtungsergebnissen des Observatoriums in
Pawlowsk beweisen. Nach den dort mitgetheilten Beobacbtungen
iiber die Temperatur und Feuchtigkeit der Sale des unterirdischen
Gebaudes fur Variations-Beobachtungen betragt die durchschnitt-
licbe Schwankung der Temperatur daselbst im Laufe des Tages
nur ± o,°o7, d. h. eine bei der Reduction der Beobachtungen ganz
zu vernachlassigende Grosse. Was aber die Feuchtigkeit betrifft,
so hatten wir Dank der hohen constanten Saal-Temperatur von
21 (seit 1 891: 20 ) mit einer mittleren Variation von bloss it 0^25
im Laufe eines Monats und von ± o,°50 im Laufe eines Jahres
von Anfang an, wenigstens im Magnetographen-Saal, nie zu leiden.
Erst als im Magnetometer-Saal (wie sich spater zeigte in Folge einer
schadhaften Stelle im ausseren Gewolbe) die Feuchtigkeit anfing
storend zu werden, d. h. im Sommer 1885 bis 90 Proc. der Satti-
gung erreichte, wurden regelmassige und genaue Feuchtigkeits-
Beobachtungen mit Ventilations-Psychrometern in beiden Salen ein-
gerichtet und publicirt. Zugleich suchte ich durch Anlegung von
Biskellern vor den Oeffnungen der Luft zufiihrenden Kanale eine
Verminderung der Feuchtigkeit im Magnetometer-Saal zu erzielen,
da ich dieselbe damals noch ausschliesslich der theilweisen Conden-
sation von im Freien bei iiber 21 mit Wasserdampf gesattigten
Luft nach ihrem Eindringen in diesen Saal zuschrieb. Seit dieser
Zeit bis und mit 1893 stieg dann nach den in den Einleitungen mit-
geteilten Daten die relative Feuchtigkeit im Magnetographen-Saal
nicht mehr iiber 76 Proc. und im Magnetometer-Saal nicht
iiber 85 Proc. Erst im August 1894 erreichte sie im letzte-
ren, nach einem nassen Sommer, wieder 91 Proz., wo dann auch
durch Ablosen des Bewurfs an der innern Saaldecke die Schadhaf-
tigkeit des Gewolbes offenbar wurde. Nach erfolgter Reparatur im
Sommer 1895 1 g* n g avich hi er die maximale Feuchtigkeit wieder
unter 85 Proc. zuriick.
Entweder sind also unterirdische Gebaude fur Variations-Appa-
rate bei einfacher Construction derselben den Gefahren der Feuch-
tigkeit und ungeniigender Temperatur-Constanz unterworfen oder
sie erheischen zur Vermeidung der letzteren complicirte, kostspie-
lige Anlagen, einen theuren Unterhalt und sehr sorgfaltige Ueber-
wachung der Beheizung. Es schien mir daher die Frage nicht
iiberfliissig, warum man iiberhaupt gerade die Variations- Apparate
1 Nach AbgTaben der Erdschicht vom ausseren Gewolbe an dieser Stelle zeigte
sich namlich, dass dasselbe dort aufeine grossere Strecke hin statt mit Cement, wie
sonst iiberall, nur mit Kalk-Mortel geraauert und bedeck t war, welch letzterer sick
durch das eingedrungene Regenwasser allmahlich aufgelost hatte.
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VOLLSTANDIGE MAGNETISCHE OBSERVATORIEN 163
in unterirdische Raume verlegt babe, wahrendman sich fur die ab-
soluten Messungen durcbweg mit oberirdiscben zum Theil sehr
einfacben Bauten begniigte, obscbon ja fur die beiderlei Beobach-
tungen die Abhangigkeit des magnetiscben Moments der Magnete
von der Temperatur eine Rolle spielt und deshalb bei beiden zur
Erzielung reiner erdmagnetischer Resultate Reductionen auf
gleiche Temperatur zu erfolgen baben. Nun sind bei den absolu-
ten Bestimmungen der Horizontal-Intensitat zu dem Ende ja nur
wenige unmittelbare Beobacbtungsdaten auf eine gemeinsame Tem-
peratur zu reduciren, wabrend fur die fortlaufenden Beobachtungen
oder gar Registrirungen der beiden Intensitats-Variometer diese
Reductionen bei fortwahrend variirender Temperatur eine unend-
licbe Miihe verursachen wiirden. Fur diese letzteren musste man
daber besonders nach Mitteln zur Verminderung sei es der Tem-
peratur- Variationen sei es der Abhangigkeit des Stabmagnetismus
von der Temperatur suchen. Dabei kamen aber offenbar nocb
einige andere Umstande in Betracht als nur die Grosse der Reduc-
tions-Arbeit, namlich auch die Moglichkeit ihrer genauen Ausfuh-
rung. Je grosser namlich die Amplitude der Temperatur- Aende-
rung bei den Beobachtungen ist, desto genauer muss der Tempera-
tur-Coefficient der Magnete bestimmt werden, und je bedeutender
der absolute Werth des letztern ist, um so sicherer ist die Tempe-
ratur der Magnete zu ermitteln. Beides bat seine grossen Schwie-
rigkeiten und zwar hauptsachlich deshalb, weil ein in der Nabe
des Magnets befindliches Thermometer die wirkliche augenblick-
liche Temperatur des Magnets nur unter besondern Vorsichtsmass-
regeln und jedenfalls nur bei sehr langsamer Aenderung der Tem-
peratur der nachsten Umgebung genau angeben wird. Man hat
haufig nicht genugsam beachtet, dass der letztere Umstand auch
bei den absoluten Intensitats-Messungen eine wichtige Rolle spielt,
wie man denn iiberhaupt erst in neuster Zeit von der Meinung
zurtickgekommen ist, es sei fur die absoluten Messungen eine viel
geringere Genauigkeit als fur die Variations-Beobachtungen ausrei-
chend. Aus alien diesen Griinden bestrebte man sich also fur die
Variations-Apparate einmal Raume mit wenig und jedenfalls sehr
langsam variirender Temperatur zu gewinnen und anderseits durch
Compensation den Einfluss der letzteren auf den Stabmagnetismus
im Resultat zu vermindern. Was die Temperatur-Compensation
der Intensitats-Variometer — Bifilar-Magnetometer und Lloyd'sche
Wage — betrifft, so sind erst in neuster Zeit solche Methoden da-
fur gefunden worden, welche eine genugend iibereinstimmende
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164 &- WILD LVol. iv, no. 3.]
Temperatur der Magnete und der Compensations- Vorrichtung —
immerhin bei nicht allzuraschen Temperatur-Aenderungen — ga-
rantiren und somit als allgemein wirksam bezeichnet werden kon-
nen. Eine vollkommene Temperatur-Compensation, welche also
jede Reduction ausschliessen wiirde, ware indessen nur durch lan-
geres, sehr zeitraubendes Ausprobiren zu erzielen und so begniigt
man sich denn durchweg mit einer gewissen Annaherung. Es
muss also doch fur die Reduction die Temperatur der Magnete,
wenn auch minder genau, bestimmt werden und ist deshalb,
wie auch behufs richtiger Function der Compensation fur die
Variometer doch ein Local mit moglichst constanter Temperatur
erwunscht
Es lag nahe, zu dem Ende zuerst an kellerartige, unterirdische
Raume zu denken, da theoretisch schon in 1 m. Tiefe unter der
Erdoberflache die tagliche Periode der Temperatur ganz unmerk-
lich wird, welcher Umstand die Anbringung einer constanten Tern-
peratur-Reduction bei den Variometern wenigstens im Laufe jeden
Tages ermoglichen und damit bereits die Reductions- Arbeit wesent-
lich vermindern wiirde. Die nothwendige Ventilation der unterir-
dischen Raume und deren Beheizung, namentlich im Sommer zur
Verhiitung allzugrosser Feuchtigkeit, stort aber im Allgemeinen,
wie wir gesehen haben, das Zustandekommen einer ganz befriedi-
genden taglichen Temperatur-Constanz. Gewohnlich verzichtet
man darauf, eine solche auch fur das Jahr anzustreben, so dass z. B.
die jahrliche Temperatur-Schwankung in den unterirdischen Rau-
men zu Potsdam ±5° und zu Pola ±3° betragt. Wollte man aber
eine constante Temperatur fur das ganze Jahr unter natiirlichen
Verhaltnissen erzielen, so miisste man theoretisch bis zu Tiefen von
ungefahr 20 m. unter der. Erdoberflache gehen.
Herr Professor H. F. Weber hat bei Gelegenheit des neuen
Physikbaus fur das eidgen. Polytechnicum in Zurich (1888) zur
angenaherten Erreichung dieses Zieles auf dem abschussigen Ter-
rain an der Westseite des Hauptgebaudes vier, mit diesem durch
einen unterirdischen Corridor verbundene Sale anlegen lassen,
deren Gewolbe noch 5 — 6 m. hoch mit Erde bedeckt sind. Nach
den vom September 1894 bis August 1896 (mit einer Unterbrechung
vom Januar bis Mai 1895) s ^ c ^ erstreckenden Beobachtungen des
Herrn Dr. Kawalki, welche mir dieser giitigst mitteilte, betrug
wahrend dieser Zeit das Maximum der Temperatur daselbst I2,°5
und das Minimum io,°4, also die Jahresschwankung wenig tiber
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VOLLSTANDIGE MAGNETISCHE OBSERVATORIEN 165
±: 1 . 1 Wie wir oben bereits mitgetheilt haben, war es im Varia-
tions-Gebaude in Pawlowsk bei nur 1,5 m. Dicke der Erdschicht
dariiber Dank den doppelten Wanden und Gewolben und der un-
mittelbaren Beheizung bloss des breiten Zwischenraumes zwischen
beiden, unter Anpassung der Starke derselben an die verschiede-
nen Jahreszeiten moglich, eine Beschrankung der mittleren Jahres-
schwankung der Temperatur auf ± o,°5 bei einer taglichen von
bloss dt o,°o7 zu erzielen. Eine weit gehende Constanz der Tem-
peratur kann also hiernach auch auf anderem Wege als durch tiefes
Hineingehen in die Erde erzielt werden. Die nachstehenden Er-
fahrungen aber im Pavilion fur absolute Messungen zu Pawlowsk
zeigten mir, dass man uberhaupt gar nicht in die Erde hineinzu-
gehen brauche, um Rdume tnit hiniang/ich constanten Temperatu-
ren zu gewinnen. Im Central-Saal namlich dieses Pavilions, des-
sen Beheizung auch nicht direct, sondern durch einen ihn umge-
benden und ihn damit von der Aussenwand des Gebaudes isoliren-
den Corridor erfolgte, habe ich haufig bei Untersuchungen, welche
sich iiber 9 Stunden hin erstreckten und an denen zwei Personen im
Local sich betheiligten, nur Temperatur- Variationen von 2 bis 3
Hundertstel eines Grades gehabt. Bei einiger Vorsicht in der Be-
heizung ware es also leicht moglich gewesen, die tagliche Tempe-
ratur-Schwankung darin auf dbo,°i zu beschranken. Im Winter-
halbjahr liess man durch entsprechende Beheizung die Saal-Tempe-
ratur gewohnlich nicht unter 15 sinken, wahrend man dieselbe im
Sommerhalbjahr den Tagesmitteln der ausseren Luft-temperatur
bis gegen 25 ° einfach nachfolgen liess. In Folge davon habe
ich im Sommer nie eine hohere relative Feuchtigkeit als 80
Proz. in diesem Saal beobachtet. Hieraus folgt, dass man auch in
ganz oberirdischen Variations- G ebduden dieselben Beschrankung en der
taglichen und jdhrlichen Temperatur-Schwankung der freien Luft
auf ±l o°i pro Tag beziehungsweisse ±5° pro Jahr wird erreichen
kbnnen tvie in den gewohnlichen unterit disc hen G ebduden dieser Art t
1 Leider sind diese Raume fur magnetische und electrische Messungen deshalb
ganz unbrauchbar, wcil die Luft in ihnen theils in Folge von Condensation des
Wasserdampfes der durch Ventilationsrohren direct von aussen einstromenden Luft
im Sommer theils in Folge des Eindringens von Grundwasser an mehreren Stellen
ganz oder nahezu mit Wasserdampf gesattigt ist. So habe ich selbst im October
1897 in dem einen, anscheinend trockenen Saal 95 Proz. relat. Feuchtigkeit beobach-
tet, die etwas spater, als auch da Grundwasser eingedrungen war, auf 100 Proz. an-
stieg. Uebrigens waren gegen wart ig auch abgesehen hievon feinere magnetische
Messungen in diesen Raumen wegen der Storungen durch den allzunah vorbeige-
henden electrischen Tramway ausser von 12-5 Uhr in der Nacht unmoglich.
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1 66 H> WILD [vou iv. No. 5.)
ohne dass man dabei St'drungen durch ubergrosse Feuchtigkeit wie in
den letzteren zu bejiirchten hdtte.
Als daher im Mai 1893 Hen* Dr. Maurits Snellen, bei seinem
Besuche in Pawlowsk in Begleit des hollandischen Regiemngs-
architekten mir die Frage vorlegte, ob ich ihm fur das zu errich-
tende neue magnetische Observatorium in Utrecht zu einem ober-
oder unterirdischen Gebaude fur die Variometer rathen wiirde,
glaubte ich ihm entschieden ein oberirdisches mit Isolir-Corridor
empfehlen zu miissen. Hen* Snellen hat denn auch, wie bekannt,
diesen, seinen eigenen Ideen entsprecheuden Rath befolgt und mir
auf meine Anfrage kiirzlich brieflich mitgetheilt, dass es ihm in
der That moglich sei, die Temperatur in den Raumen dieses ober-
irdischen Variations-Gebaudes bis auf o,°i constant zu erhalten.
Wahrend aber Herr Snellen die Temperatur dieser Raume nicht
bloss pro Tag bis o,°i constant erhalten will, sondern daselbst auch
das ganze Jahr hindurch eine constante Temperatur von 18 zu
unterhalten wiinscht und zu dem Ende die Wand und Decke ausser-
halb und oberhalb des Isolir- und Heiz-Corridors noch durch eine
Torfmull-Schicht von 1,5 m. Dicke weiterhin isolirend gemacht hat,
habe ich in meinem Plan bei gewohnlicher, massiger Dicke der
Aussenwand des Gebaudes nur die Erzielung einer taglichen Texn-
peratur-Constanz von=fco,°i angestrebt und eine jahrliche Temperatur-
Schwankung der Raume von ±5°, wie im erwahnten Pavilion, zuge-
lassen,weil diese unbeschadet der Genauigkeit der Resultate ohneWei-
res eine zu hohe Feuchtigkeit der Raume im Sommer ausschliesst.
Schon diese Temperatur- Verhaltnisse im Gebaude der Variometer
werden zusammen mit wenigstens theilweiser Temperatur-Com-
pensation ihrer Magnete ganz ungemein die Bedingungen fur be-
friedigende Reduction auf eine Normal-Temperatur erleichtern.
Es sei z. B. beim Bifilar-Magnetometer der Temperatur-Coefficient
durch Compensation auf 0,5 Scalentheil pro i° C. (von etwa 2 in
uncompensirten Zustand) und bei der LloyxTschen Wage auf 1,0
Scalentheil pro i°C (statt etwa 6 in uncompensirtem Zustand)
vermindert worden, was unschwer zu erreichen ist, so entspricht
also der taglichen Temperatur-Oscillation von ±o,°i im betreffen-
den Local eine Aenderung des Bifilar-Staudes um ± 0,05 und des
Standes der Lloyd'schen Wage um ±0,10 Scalentheile, wonach die
Reductionsgrosse fur den Tag je als constant angenommen werden
kann. Es ist dann auch iiberhaupt eine Stcherheit der Tempera-
turbestimmung der Magnete von ±o,° i, welche bei der langsamen
Temperatur- Aenderung von Tag zu Tag wohl einzuhalten ist, un-
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VOLLSTANDIGE MAGNETISCHE OBSERVATORIEN 167
ter diesen Umstanden ganz ausreichend. Die jabrliche Temperatur-
Schwankung aber von ±5° um die Normal-Tetnperatur wiirde un-
ter den obigen Voraussetzungen, damit die Reduction auf diese
stets beim Bifilar bis auf ± 0,05 und bei der Lloyd'schen Wage bis
auf ±0,10 Scalentheile sicher auszufuhren sei, eine Genauigkeit
von bloss 2 Procent in der Bestimmung des Temperatur-Coefficien-
ten beider Instrumente erheischen. Diese geringe Genauigkeits-
Anforderung gestattet eine leichtere Bestimmung des letzteren auch
deshalb, weil er dann nicht mehr als von der absoluten Tempera-
tur abhangig zu betrachten ist, somit die Beriicksichtigung des
quadratischen Gliedes der Temperatur unnothig wird.
Dass Angesichts der hiemit bewiesenen Zulassigkeit einer ober-
irdischen Anlage des Variationsgebaudes dasselbe ohne Risiko ge-
genseitiger Stoning der Instrumente auch den Raum fur die nor-
malen absoluten Messungen in sich aufnehmen konne, habe ich
wohl zur Geniige durch meinen Plan und die obigen erganzenden
Bemerkungen dazu bewiesen. Nur auf einen Vortheil, den diese
Vereinigung in sich schliesst, mochte ich hier noch hinweisen. Sie
gewahrleistet namlich ohne Weiteres auch fur die absoluten Mes-
sungen die ihrer Genauigkeit fbrderliche Temperatur-Constanz,
welche ich schon oben als wiinschbar bezeichnet habe. Obschon
namlich bei den absoluten Messungen der Horizontal-Intensitat
nur die gewohnlich kleine TemperaturdifFerenz des Hauptmagnets
bei den Schwingungen und Ablenkungen eine Correction bedingt,
so mtissen die Temperaturen des Magnets, da hier keine Tempera-
tur-Compensation zulassig ist, doch recht genau gemessen werden,
wofiir eben eine sehr langsame Temperatur- Aenderung des Locals
erforderlich ist.
Ich gebe gerne zu, dass mein Plan fur die Einrichtung kunftiger
magnetischer Observatorien vom Gewohnten erheblich abweicht und
daher meine Beweggriinde dafiir, namentlich auch beziiglich des Ge-
gensatzes zu unterirdischen Anlagen, in der betreffenden Abhandlung
etwas zu kurz und unvollstandig angegeben waren. Es war mir da-
mals mehr darum zu thun, die theoretische Moglichkeit der Vereini-
gung der absoluten Messungen und der Variations-Beobachtungen
in einem Gebaude von nicht allzugrossen Dimensionen nachzuwei-
sen. Nach meinem neuen, noch nicht publicirten Plan konnen
dieselben dort angefiihrten Instrumente in einem Gebaude von
160 m. 2 Grundflache, also unter der Annahme von 5 m. Hohe, von
800 m. 8 Inhalt untergebracht werden, wobei durch die gegenseitige
Einwirkung aller Magnete aufeinander nur verschwindend kleine
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1 68 H. WILD [Vol. IV, No. 3.]
Fehler bei den absoluten Messungen — namlich kleiner als 2" bei der
Declination und Inclination und von bloss 0,000006 H. bei der Ho-
rizontal-Intensitat-resultiren und auch die Variations- Apparate
bloss um zu vernachlassigende Grossen gestort werden. Da dieses
oberirdische, also verhaltnissmassig billig zu erstellende Gebaude
Alles umfasst, was zu einem vollstandigen magnetischen Observa-
torium gehort und alle an ein solches zu stellende Bedingungen
erfullt, so diirfte mein friiherer, wie der neue Plan zur Erleichte-
rung der Anlage magnetischer Observatorien und damit ihrer Aus-
breitung in der Zukunft beitragen und somit die vorliegende, aus-
fiihrliche Begriindung desselben gegeniiber den Einwanden des
Herrn Eschenhagen wohl nicht als iiberfliissig angesehen werden.
Zurich, 5. Mai 1899.
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COMPLETES OBERIRDISCHES MAGNETISCHES
OBSERVATORIUM.
Von H. Wild.
V
In einem Artikel „Ueber die Einrichtung magnetischer Obser-
vatorien" l habe ich den Plan eines magnetischen Observatoriums
mitgetheilt, bei dem in einem einzigen oberirdischen Gebaude nicht
bloss die drei Instrumente fur absolute Messungen der Declination,
Inclination und Horizon tal- 1 ntensi tat mit ihren Magneten, sondern
auch zwei Serien von Variations-Instrumenten fur Declination,
Horizontal- und Vertikal-Intensitat (die eine Serie selbstregistri-
rend) so untergebracht waren, dass dieselben innerhalb der Ge-
nauigkeitsgrenzen bei derartigen Beobachtungen keinen storenden
Einfluss aufeinander ausuben. Die Griinde, welche mich zu dieser,
von der iiblichen abweichenden Einrichtung bewogen, habe ich
schon dort, viel ausfiihrlicher aber in meinem, in dieser Nummer
veroffentlichten Artikel: „Ueber die Moglichkeit, vollstandige mag-
netische Observatorien ganz oberirdisch und in einem Gebaude ein-
zurichten" dargelegt. Wenn man aber darnach in oberirdischen
Gebauden dieselben Bedingungen constanter resp. sehr langsam
variirender Temperatur realisiren und iiberdies die storende Feuch-
tigkeit viel leichter vermeiden kann als in unterirdischen Raumen,
warum sollte man dann nicht lieber die erstern auch fur die mag-
netischen Variations-Instrumente wahlen, und wenn man die letztern
zusammen mit den Instrumenten fur die absoluten Messungen ohne
Befiirchtung gegenseitiger Storungen bei passender Anordnung in
ein und demselben Gebaude unterbringen kann, warum sollte man
diese Bequemlichkeit aufgeben und sie durchaus auf zwei Gebaude
vertheilen wollen? Diesen Erwagungen zufolge dtirfte es daher
den Lesern dieses Journals nicht unlieb sein, die am letzern Ort
bereits erwahnte zweite, in mehrern Beziehungen vortheilhaftere
Losung des fraglichen Problems kennen zu lernen.
Von den beiden beiliegenden Tafeln stellt Tafel I einen Grund-
riss und Tafel II einen Aufriss des fraglichen Gebaudes dar. Wie
man sieht, besteht dasselbe aus zwei nahe gevierten Salen Pxind P\
in welchen die zwei Serien von Variations-Instrumenten aufgestellt
1 Bulletin de VAcad. Imp. des sciences de Si. PHersbourg, T. VIII, No. 3. Mars
1898. p. 191.
4 169
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170 H. WILD [Vou. iv, No. 3.]
sind, und einem schmalen aber langen Saal zwischen ihnen, der die
Instrumente fur absolute Messungen enthalt.
Ehe ich auf eine Beschreibung der Construction und Einrichtung
des Gebaudes eintrete, will ich in erster Linie die gegenseitige Ein-
wirkung der Instrumente bei der angenommenen Anordnung unter-
suchen und feststellen. Im Saale P befindet sich auf dem mit £/be-
zeichneten Pfeiler ein Unifilarmagnetometer, auf dem Pfeiler L eine
Lloyd'sche Wage und auf dem Pfeiler B ein Bifilarmagnetometer,
deren Magnetspiegel-Stande vom Sitz in a aus an den Scalen in .S'oder
s abgelesen werden konnen. Entsprechende Variations-Instrumente
sind im Saale P f auf den Pfeilern U\ V und B' aufgestellt, die
von al aus beobachtet und beleuchtet werden und in / s' ihre
photographischen Registrirer und Scalen besitzen. Im mittleren
Raum habe ich fur die absoluten Messungen auf dem Pfeiler D das
Declinatorium, in / ein Inductions-Inclinatorium und auf dem
Pfeiler H ein Instrument fur die absoluten Messungen der Hori-
zontal-Intensitat nach der Gauss'schen Methode angenommen. Das
zum Inductions-Inclinatorium gehorige Galvanometer sei auf dem
Pfeiler G placirt, besitze aber ein sehr nahe vollkommen astasirtes
Magnet-Paar, so dass seine magnetische Fernwirkung als ver-
schwindend anzunehmen ist. Bezogen auf den Mittelpunkt / des
Gebaudes und eine durch die Verbindungslinie D H dargestellte
X~Axe (positiv von /nach Siid gerechnet), sowie eine K-Axe LL'
(positiv von / nach West gerechnet), sind die Ordinaten der Magnet-
Mittelpunkte aller Instrumente, die sammtlich als in der gleichen
Horizontalebene liegend angenommen sind, folgende in Meter
ausgedriickt :
X
y
X
y
von D
: —4.0
0.0
von H
: +4.0
0.0
von U
— 2.0
+ 5-5
von {/'
— 2.0
— 5-5
von L
0.0
+ 6.0
von L!
0.0
— 6.0
von B
-f- 2.0
+ 5.5
von ff
+ 2.0
— 5-5
Wie in der ersten Abhandlung setze ich ferner voraus, es be-
sitzen die Magnete dieser Instrumente folgende magnetische Mo-
mente in mm., mg., s. :
die Magnete der 3 Variometer je : 1.2 X 10 7
der Hauptmagnet des Apparats
fur abs. Intensitatsmessung und
der Magnet des Declinatoriumsje : 2.0 X 10 7
der Hiilfsmagnet des Apparats
fur Intensitatsmessung : 0.5 X 10 7
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OBERIRDISCHES MAGNET. OBSERVATORIUM 171
Nehmen wir endlich ebenso wie in der ersten Abhandlung an,
dass das Gebaude nach dem magnetischen Meridian orientirt sei,
also die Verbindungslinie der Pfeiler D und H oder die -Y-Axe
des Coordinaten-Systems parallel demselben sei, die Magnete der
Lloyd'schen Wagen ebenso parallel dem magnetischen Meridian
mit Nordpol nach Nord orientirt und die Nordpole der Bifilar-
magnete nach Osten gewendet seien, endlich dass die Inclination
1 = 63°
und die Horizontal-Intensitat in denselben Gauss'schen Einheiten
wie die magnetischen Momente (mm., mg., s.) sei :
H=2.o ,
so sind alle Elemente gegeben, um nach den Gauss'schen Formeln
die gegenseitige Einwirkung der Magnete zu berechnen.
Unter den obigen Beschrankungen ist namlich die Einwirkung
eines, im Anfangspunkt der Coordinaten befindlichen Magneten
vom magnetischen Moment M auf die zu bestimmenden Elemente
des Erdmagnetismus in einem um r von seinem Centrum entfernten
Punkt, wenn die Verbindungslinie beider das Azimut g von Slid
nach West gerechnet besitzt, gegeben durch :
a) wenn der wirkende Magnet parallel zum magnetischen Meri-
dian orientirt ist :
*H _ M , f .
77 = "*" 777» (l ~~" 3cosV) >
-^- = -+-7^2(1 — 3 cos V) >
o . M sin 2 i , q .
T ~H? ' ~~2~~ ^ — 3 COS ^ '
wo Also 8/?, 8/7, 8Zund 8i die bewirkten Veranderungen der De-
clination D (+ Vermehrung der westlichen Declination), der Hori-
zontal-Intensitat //, der Vertikal-Intensitat Z und der Inclination i
(-f- Vermehrung der Neigung des Nordpols unter den Horizont)
darstellen und das obere Zeichen bei normaler, das untere aber bei
verkehrter Lage des Magnets im Meridian gilt.
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172 H. WILD [Vol. IV, No. 3.]
b) wenn der wirkende Magnet senkrecht zum magnetischen
Meridian orientirt 1st :
M •
dD==qz 7/>a ( l — 3 sin V) »
&// __ M 3 .
8Z 8/f a . dn 2/ 8^/
wo das obere Zeichen fur eine Magnet-Lage mit Nordpol nach West
gewendet und das untere fur eine solche mit Nordpol nach Ost ge-
wendet gilt.
Die verschiedenen vorkommenden Combinationen der bestandig
in gleicher Stellung verbleibenden Magnete der Variationsapparate
(abgesehen von ihren kleinen Bewegungen bei den Variationen,
die ohne erheblichen Einfluss auf die andern Instrumente sind) zu
den Magneten der Instrumente fur absolute Messungen sind nun :
1. Zustand in den Intervallen zimschen den absoluten Messungen,
wo der Declinatorium-Magnet in D normal im magnetischen Meri-
dian und der Hauptmagnet sowohl als der Htilfsmagnet des Inten-
sitatsapparats beide in h ebenfalls in normaler Lage im magneti-
schen Meridian sich befinden. (Dass der letztere sich in Wirklich-
keit nicht genau im Punkte //" wie der erstere, sondern etwas seitlich
befindet, ist fur das Resultat nicht von Belang.) Die storende
Einwirkung dieser drei Magnete auf die Variometer ist dann :
auf das Unifilar in U : dD = — 2".23 ,
„ „ „ „ u* \ 8Z>' = + 2.2 3 ,
O tt Cx rrf
auf die Bifilare in B \x.B f : -?y = -yjj = — 0.0000261 ,
ri Jti
auf Lloyd's Wagen in Lvl.U: —=■ = -yr = — 0.0000080 .
Da auch die Variometer untereinander noch gegenseitige Sto-
rungen ausiiben, welche wir ebenso wie die vorstehenden als con-
stant annehmen konnen, so ist es moglich, von den so modificirten
Standen derselben als den normalen, durch die absoluten Messungen
ihrem Werthe nach zu bestimmenden auszugehen, und wenn die
Empfindlichkeits-Coefficienten der Variations- Instrumente ebenfalls
in der oben fixirten Gegenwart der Magnete der absoluten Instru-
mente stattfinden, so kann auch in dieser Beziehung der obige Zu-
stand als der normale gelten.
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OBERIRDISCHES MAGNET. OBSERVATORIUM 173
2. Zustand bei den absolute*. Declinations- Messungen. Die Magnete
sollen sich hiebei unverandert in derselben Lage wie vorhin be-
finden. Der Einfluss auf die Variations-Instrumente ist also auch
derselbe wie gewohnlich und es werden daher die absoluten Decli-
nations-Bestimmungen nicht bloss den augenblicklichen Normal-
stand des Unifilar-Magnetometers, sondern einen auch fur alle
Beobachtungen um diesen Zeitpunkt herum giiltigen Werth des-
selben ergeben.
Es fragt sich also jetzt nur, inwiefern die so in D gemessene
Declination in Folge des Einflusses aller Variationsapparate und
der beiden Magnete des Intensitatsapparats in H von der wahren ab-
weichen wird. Die letztere ist, wie unmittelbar ersichtlich, gleich
Null und die algebraische Summe der Wirkung aller sechs Variations-
apparate auf die Declination in D berechnet sich nach unsern For-
meln zu:
8Z> A =-i".6 5
d. h. die gemessene absolute Declination, wenn sie eine westliche
ist, wird gegeniiber der wahren um i".65 zu klein ausfallen.
3. Zustand bei den absoluten Inclinations- Messungen, Die beiden
Magnete des Intensitatsapparats in H bleiben unverandert in ihrer
normalen Lage im Meridian, dagegen wird der Magnet des Declina-
toriums in D um 180 umgekehrt, so dass sein Nordpol jetzt nach
magnetisch Siid weist.
Die storende Wirkung dieser drei Magnete auf die Variometer
berechnet sich jezt zu :
auf das Unifilar in U : dD = + i6".2i ,
„ „ „ „ u 9 \ dz?=- 16.21 ,
Q TT O TTl
auf die Bifilare in B u. B' : —rj = -777- = — 0.0000489 ,
ri ri
auf Lloyd's Wagen in L u. L! : —=- = —=r = — 0.0000008 .
Die DifiFerenz dieser Grossen und der unter 1. angegebenen wird
also die Veranderungen ergeben, welche die angenommenen Nor-
malstande der Variationsapparate durch die neue Combination er-
fahren ; sie werden somit sein :
in U : 8 D t = + i8".44 in U' : 8ZT, = — 18*44 •
in B u. B : —jy- = ZJ , = — 0.0000228 ,
rti ri i
T r , dZ,- dZ' t -
in L u. L : -=— = -^7— = + 0.0000072 .
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174 H - WILD [vol. nr, no. 3 ]
Wahrend der Dauer der Inclinations-Messungen erleiden also
die Unifilar-Magnetometer eine erhebliche Standanderung, z. B. von
0.3 Scalentheilen, wenn der Bogenwerth eines Scalentheils bei ihnen
eine Minute ist. Indem man dieselben unmittelbar vor und nach
erfolgter Umkehr des Declinations-Magnets zu Anfang und am
Schluss der Inclinations-Messungen abliest, kann mani ndessen den
Betrag dieser Stoning leicht empirisch ermitteln und, wenn nothig,
an den Angaben der Unifilare wahrend dieses Zeitintervalls als
Correction anbringen.
Die beiden andern storenden Einwirkungen sind verhaltniss-
massig geringer, influiren aber auf das Resultat der Inclinations-
messung und sind daher gemeinsam mit dem Fehler dieser abso-
luten Messung zu betrachten, der durch den gemeinsamen Einfluss
der sammtlichen Variationsapparate und der drei Magnete der abso-
luten Instrumente in D und H bei ihrer jetzigen Lage auf die In-
clination in i bedingt wird. Dieser Fehler berechnet sich zu :
8i=-i".34,
d. h. die nordliche Inclination i wird um i".34 zu klein durch unsere
absolute Messung erhalten werden.
Nun wird die absolute Messung der Inclination nicht unmittel-
bar als solche benutzt, sondern dient dazu, aus ihr und der gleich-
zeitigen durch das Bifilar-Magnetometer gegebenen Horizontal-
Intensitat die Vertikal-Intensitat Z nach der Formel :
Z = H tang i
zu berechnen, um mittelst dieser Grosse den Werth des Normal-
standes der Lloyd'schen Wagen zu bestimmen. Aus den fehler-
haften Angaben fur H und i in Folge Einwirkung der anderen
Magnete resultirt aber fur Z als Fehler :
dZ=tangi.df/+-~.di ,
cos 8 z
oder :
Z H "*" sin 21 '
so dass man in Anbetracht der oben angegebenen Aenderung der
Vertikal-Intensitat in L und ZJ zur Zeit der Inclinations-Messung
gegeniiber der als normal angenommenen als Summe 2 aller Fehler
von Z hat :
2dz__dz d/f 2
z ~ z +-J7 + s^7T 8/ -
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OBERIRDISCHES MAGNET. OBSERVATORIUM 175
Setzen wir hier die obigen Werthe ein, so kotnmt :
Z* Zi
7 — O.OOOO3I7 .
Es ist also strenggenommen zur Berechnung des wahren Normal-
standes der Lloyd'schen Wagen aus den Ablesungen an ihr an der
Vertikal-Intensitat Z',-, wie sie aus dem unmittelbaren Resultat der
Inclinations-Messungund den Ablesungen anBifilar-Magnetometern
berechnet worden ist, eine Correction anzubringen, um die wahre
Vertikal-Intensitat Zi zu fin den. Es ist namlich :
Zi = Z\ (1 +0.0000317) .
3. Zustand bei den absoluten Messungen der Horizontal- Intensitdt.
Wegen der verschiedenen Lagerung der Magnete bei den beiden
Operationen, aus denen sich eine absolute Intensitats-Messung zu-
sammensetzt, muss man hier die letztern auseinanderhalten.
a) Ablenkungs-Beobachtungen. Der Declinations-Magnet ist hie-
bei in D in verkehrter Lage im Meridian zu orientiren wie bei den
absoluten Inclinations-Messungen, von den Magneten zur absoluten
Intensitats-Messung in H sei der Hiilfsmagnet normal im Meridian
und der Hauptmagnet als ablenkender Magnet senkrecht zum Me-
ridian orientirt mit Nordpol einmal nach West und sodann nach
Ost gewendet. Der Einfachheit wegen nehme ich zunachst an, beide
Magnete befinden sich hiebei sehr nahe im Punkte H und die Ab-
lenkung des Hiilfsmagnets aus dem Meridian sei als sehr klein zu
vernachlassigen.
Sammtliche Variationsapparate und der Declinations-Magnet in
D (verkehrt) haben zusammen aufdie Horizontal- Intensitat in H den
slorenden Einfluss:
dH a
-ST = _ 0-0000273 ,
und fur die Variationsapparate berechnet sich die storende Einwir-
kung der drei Magnete der absoluten Instrumente in ihrer jetzigen
Lage zu :
in U : dD = + io".62 ± i"-38 ,
in U' : 8ZT = — 10.62 ± 1.38 ,
dH
in B : — - = — 0.0000189 ±0.0000446 ,
MM
dH'
in B : -r,,- — — 0.0000189 =P 0.0000446 ,
Ml
. r 9Z
in L : -y = + 0.0000024 ±: 0.0000715 ,
. F , dZ' .
in L : -=r = + 0.0000024 -♦- 0.0000715 ,
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176 H- WILD [vol. iv. No. 3-]
wo bei den zweiten Zahlen rechts vom Gleichheitszeichen je das
obere Zeichen gilt, wenn der ablenkende Hauptmagnet in H seinen
Nordpol nach West gewendet hat, und das untere Zeichen der nach
Ost gewendeten Lage des leztern zukommt.
Um die Veranderungen zu erfahren, welche die angenommenen
Normalstande der Variationsapparate durch die jetzige Combination
erfahren, haben wir von obigen Grossen wieder die unter 1. gege-
benen abzuziehen und erhalten so :
in U : 8Z>a, = — I2".85 ± i"-38 ,
in If : d/y^ = + 12.85 ± 1.38 ,
- n d &<h
in B : -7J- 1 = + 0.0000072 ± 0.0000446 ,
9 W
in B : ——^= -f- 0.0000072 T 0.0000446 ,
r dZa. .
in L : -7T- 1 ~ + 0.0000104 ± 0.0000715 ,
Z.a x
fay
in LI : — =-^ = +0.0000104 ^ 0.0000715 .
Da es bei Reduction der beobachteten Ablenkungswinkel
am Hiilfsmagnet auf constante Declination nur auf die Differenzen
der Declinations- Variationen ankommt, so ist die obige constante
Storung der Unifilar-Magnetometer von 1 2.^85 ohne Einfluss auf
diese Reductionen und die variable Storung von ± i."38, welche die
Ablenkungswinkel um diesen Betrag falschen wiirde, ist als sehr
klein zu vernachlassigen.
Die Storung an den Lloyd'schen Wagen hat auf die Intensitats-
Messung keinen Einfluss und ware wie jene am Unifilar-Magneto-
meter nur in dem unwahrscheinlichen Fall zu beriicksichtigen, wo
gerade fur diese Zeit die Kenntniss der absoluten Declination oder
Vertikal-Intensitat erfordert wiirde.
Die constante storende Einwirkung auf die Bifilare werden wir
im Folgenden zusammen mit denjenigen bei den Schwingungs-
beobachtungen erortern ; die variable Grosse aber ± 0.0000446 hebt
sich bei den Reductionen der beobachteten Ablenkungen auf con-
stante Intensitat heraus.
b) Schwingungs-Beobachtungen. Der Declinationsmagnet werde
hierbei in D wieder in die normale Lage im Meridian zuriickge-
gebracht, und der Hiilfsmagnet unmittelbar neben ihm in verkehr-
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OBERIRDISCHES MAGNET. OBSERVATORIUM
177
ter Stellung (Nordpol nach Siid gewendet) hingelegt, wahrend also
der Hauptmagnet in H in nonnaler Lage im Meridian sich befindet.
Die storende Einwirkung sammtlicher Variationsapparate, so-
wie des Declinations- und Hiilfsmagnets in D auf die Horizontal-
Intensitat in H ist jetzt :
- z T- = +O.OOOO4I I
rib
itnd diejenige auf die Variationsapparate durch die Magnete der
absoluten Instrumente wird:
in U : BD =— i". 3 2 , in U' : 8ZX = + i". 3 2 ,
m Bu.B : -vp =~- -r>r = — 0.0000214 ,
inZu,L : -y- ~—=r= — 0.0000056 .
Ziehen wir hievon wieder die betreffenden Grossen unter 1. ab,
so erhalten wir die Veranderungen der angenommenen Normal-
stande der Variationsapparate in Folge dieser neuen Combination,
namlich :
in U:dBp = -\-o".9i , in U' : 8Z>'/? - — o".9i ,
in Bu.B : -^- ===-^== + 0.0000047 ,
. . ., dzp dz'p .
in Lvl.L : -~- = —^,- - = + 0.0000024 .
Zp Z fi ' ^
Die Aenderungen bei den Unifilar-Magnetometern und ebenso
die bei den Lloyd'schen Wagen, die zwar auf die Intensitats-
Messung bei den Schwingungen gar nicht in Betracht kommen,
sind iiberhaupt als sehr klein in diesem Fall ganz zu vernachlassigen.
Die Berechnung der Horizontal-Intensitat erfolgt durch Combi-
nation der beiderlei Da ten, welche die Schwingungs- und Ab-
lenkungs-Beobachtungen liefern. Heissen wir H a die wahre, fehler-
freie Horizontal-Intensitat zur Zeit der Ablenkungs-Beobachtungen
und das Mittel der Ablesungen am Bifilar-Magnetometer wahrend
derselben : m a% ferner Ht, die wahre Horizontal-Intensitat zur Zeit
der Schwingungs- Beobachtungen und das Mittel der Ablesungen
am Bifilar-Magnetometer wahrend derselben : m^ so gelten fur die
beiden Beobachtungen in H, in Beriicksichtigung der berechneten
5
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1 78 H. WILD 1 vol. iv, No. 3.)
Storungen 9 H a und 97/* daselbst durch die Magnete, offenbar die
beiden Gleichungen :
H a + %H a = A . M ,
Mo
wo M das magnetische Moment des Hauptmagnets bei o° und
A und B durch die Messungen gegebene Zahlengrossen reprasen-
tiren; und fiir die Bifilar- Magnetometer erhalt man fur dieselben
Zeiten, beriicksichtigend die bei ihnen stattfindenden Storungen,
die Gleichungen :
H a + 9//«, = = // [1 +k(m a — m a )] ,
M a +dHr- H li+k(m b — mo)^ .
wo H Q die dem Scalentheil m am Bifilar entsprechende Horizontal-
Intensitat, der Werth des sogenaunteu Normalstandes, und k den
Empfindlichkeits-Coefficient des Bifilars darstellen.
Aus den beiden ersten Gleichungen folgt :
J/ a /J a + /f a d// d + // o d// a + d/f a d// =rA.B ,
und aus den beiden letztern :
H a H b + H k(m a — f» b ) — {PHa x —*Hft.
Setzen wir diesen Werth von H a oben em und beriicksichtigen,
dass 9 Ha x , 9 H D , 9 Ha x uud 9 //J sowie H k{m a — m D ) kleine Grossen
sind, deren Producte als sehr klein zu veruachlassigen sind, so
kommt mit geniigender Annaherung:
ml ,9^+9//* 9^-97/n
/7 M I+ //, H~ I '
- A.B.[i-"° k(f %- m) ].
Wegen der Kleiuheit der Glieder in den Klanimern kann man
da Hi, - H a = H setzen und erhalt so schliesslieh :
Die Grosse unter dem Wurzelzeichen reprasentirt aber einfach
die in iiblicher Weise aus den beiderlei Beobachtungen berechnete
Horizontal- Intensitat zur Zeit der Schwingungsbeobachtungen.
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OBERIRDISCHES MAGNET. OBSERVATORIUM
1 79
Heissen wir diese H'b . so ist also unter Beriicksichtigung der
gegensdtigen Storungen der Magnete die wahre Intensitat Hb zu
dieser Zeit gegeben durch :
Fiihren wir hier fur -^ etc. die oben ermittelten Zahlenwerthe
Ha
ein, so kommt:
Hb = H'b[i — 0.0000056] .
Es ist also H't X 0.0000056 die am unmittelbaren Resultat der
Intensitats-Messung anzubringende Correction, um die wahre un-
gestorte Horizontal-Intensitat Hb zu erhalten. Mit diesem Werth
von Hb ist dann mittelst der Gleichung S. 178 :
BHp
Hfi
der Werth H des Normalstandes m des Bifilars zu berechnen.
• H b[ l +^) = H oli+k(m a --m )']
Zur Beurtheilung der so berechneten Fehler ist es nbthig, sich
iiber die bei magnetischen Messungen anzustrebenden Genauig-
keiten zu verstandigen.
In meinem Artikel : ,,Zweckmassige Empfindlichkeit der mag-
netischen Variationsapparate 44 1 habe ich den motivirten und dann
auch ziemlich allgemein adoptirten Vorschlag gemacht, diese Em-
pfindlichkeit besonders bei Magnetographen so zu normiren, dass
der Werth eines Scalentheils (mm.) sei :
fur die Declination : 1 '
fur die Horizontal-Intensitat : 0.0005 / Gauss'sche Einheiten
fur die Vertikal-Intensitat : 0.0005 ( mm., mg., s.
Da man nun 0.1 Scalentheile noch sicher schatzen kann, so
wiirde hieraus, wenn wir, wie oben angenommen, H=2.o und
Z= 3.9 setzen, fur die Genauigkeitsgrenzen der Variationsapparate,
welche wir auch als solche fur die absoluteh Messungen annehmen
wollen, folgen:
dD =:= ± o.i'-- zh 6" ,
dff
H
az
z
1 Bulletin de VAcad. Imp. des sciences deSt. Pelersbourg, T. XXVIII, p. 30, 1881.
—fj- = rfc O.OOOO25
J~i
~y- = =t O.OOOOT3
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Die Yerg'ekhung ergiebt nun, dass selb>t dcr Feklrr der absolu-
ten DtcJ:na!icns-Mtss**c in Fol^e der gegenseitigen Wirkung der
Magnete in unserem Gebacde : cD± - — i."65 wenig mchr als ein
Viertel dcr obigen Grcnze betray also ganz zu remachlassigen ist.
Die Variationsapparate werden hieri^ri gar nicht gestdrt-
Bei der absoluten Jnt.'zrwtu^s-.lf'ssung ist die Beeinflussung der
Variationsapparate fur die Intensitat nach S- 173 anch kleiner als die
obigen Grenzen. dagegen rur das Uriifilar- Magnetometer drei Male
grosser, ist so in it empirisch, wie dort angegeben. zu ermitteln und
coth:gen Falls als Correction anzubringeu.
Ebenso ist nach S. 175 die ans derabsoiuten Inclinadonsmessnng
and der Angabe der Bifilar-Magnetometer and der Lloyd* schen
Wa^e abzuleitende Vertikal-Intensitat um eine Grosse zu corrigi-
ren. welche die obige Grenze um das 2 1 --fache uberschreitet.
Die*e Correction wird indessen illusorisch, da, wie ich an anderer
Stelle gezeigt habe 1 . bei den vollkommensten Instrnmenten sowohl
fur die Variation en als fur die absoluten Bestimnrangen der mag-
netischen Elemente zur Zeit der Fehler der absoluten Inclinations-
Be^timmucg noch mindestens — 2" betragt und derjenige der
Variometer fiir die Vertikal-Intensitat noch mindestens dem Werth
von 0.3 Scalentheil 'statt 0.1. wie oben angt-nommen) entspricht.
Wir konnen also sagen, dass auch bei der absoluten Inclina-
tion sbestimmung in unserm Gebaude weder bezuglich des absoluten
Inclinationswerthes noch bei den Variationsapparaten fur Horizon-
tal- und Vertikal-Intensitat durch die gegenseitige Einwirkung der
Magnete Fehler bedingt werden. welche die gegenwartige Leis-
tungsfahigkeit der besten magnetischen Instrumente uberschreiten.
Zur Zeit der absoluten Aftssungm der Horizontal- Intensitat wer-
den weder bei den Schwingungs- noch bei den Ablenkungs-Beob-
achtungen die Variometer fiir die beiden Intensitats-Componenten
in einer Weise durch die anderen Magnete gestort, welche obige
Grenzen erreicht. und ebenso erreicht auch der dadurch bedingte
Fehler der absoluten Messung nur den vierteu Theil jenes Betrags.
Dagegen erleidet bei den Ablenkungs-Beobachtungen das Uni-
filar eine constante Stoning, deren Betrag die obige Grenze um das
Doppelte uberschreitet- Als solche kann sie aber empirisch genan
ermittelt und in dem unwahrscheinlichen Fall, dass gerade fiir diese
Zeit ein absoluter Werth der Declination aus den Angaben der Uni-
' H. Wild. Das Kerns tan ti now* sck* witUorol. und mag~nrf. Obserpaiorimm in
Pauiausk. S. 104 u- iu f 112 n. 113. St. Petersburg 1895: siehe aock diese Zeit
schrift Vol. II. S. 103; Sept. 1897.
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OBERIRDISCHES MAGNET. OBSERVATORIUM 181
filarmagnetometer abzuleiten ware, als Correction an diese ange-
bracht werden.
Es versteht sich wohl von selbst, dass die Voraussetzungen,
welche ich bei den obigen Berechnungen gemacht habe, in Wiik-
lichkeit nicht immer streng erfullt sein werden. Zunachst wurde
vorausgesetzt, dass alle Magnete in derselben Horizontal-Ebene
sich befinden nnd ebenso auch die Mitte der Inductor-Rolle beim
Inductions-Inclinatorium. Diese Bedingung diirfte nicht unschwer
zu erfiillen sein, sind aber Abweichungen davon unvermeidlich,
so ist die Einwirkung nach den Gauss'schen Formeln fur diesen
Fall besonders zu berechnen. Sollte z. B. der Mittelpunkt der
Inductor-Rolle des Inductions-Inclinatorium in / erheblich iiber-
oder unterhalb die Horizontale durch den Declinations-Magnet in
D und den Hauptmagnet in H fallen, so ergibt eine dies beriick-
sichtigende Berechnung, dass unsere oben erhaltenen Resultate
fiir die absolute Inclinationsmessung, durch diese modificirte An-
ordnung, bis auf sehr kleine Grossen ganz unverandert bleiben.
Des Fernern habe ich angenommen, die Magnete aller drei Va-
riations-Apparate der einen und andern Serie seien gleichartige
und ihr magnetisches Moment je gleich i. 2 X io 7 . Ich habe dabei
speciell die nach meinen Angaben von M. Th. Edelmann in Mun-
chen angefertigten Variations-Instrumente, welche ich seiner Zeit
beschrieben habe, 1 im Auge gehabt, da sie diesen Bedingungen
entsprechen und sich im Observatorium zu Pawlowsk als vorziig-
lich bewahrt haben. Ganz besonders mache ich hier noch darauf
aufmerksam, dass wegen der Gleichheitdes Magnets der Lloyd'schen
Wage mit dem des Unifilar- Magnetometers die iibliche Empfind-
lichkeits-Bestimmung der erstern durch Ablenkungen an ihr und
am Unifilar unmittelbar richtige Resultate liefert, was nicht der
Fall ist, wenn die Lloyd'sche Wage einen auders geformten Magnet
besitzt. Grossere Abweichungen von dem oben angenommenen
Werthe des magnetischen Moments bei den drei Magneten waren
selbstverstandlich durch eine specielle Berechnung zu beriicksich-
tigen und dasselbe gilt auch, wenn der Declinationsmagnet und
Hauptmagnet des Intensitatsapparats erheblich andere magnetische
Momente als 2X io 7 haben sollten oder die Inclination und Horizon-
tal-Intensitat andere als die S. 170 angenommenen Werthe am Ort
der Beobachtung besitzen wiirden.
Die in der Tafel I und ebenso bei unserer Berechnung vorausge-
1 H. Wild, Neue Form magnetischer Variationsinstrumente etc. Mlm. de
l'Acad. Imp. des sc. de St. P^tersbourg. VII. se>ie, T. XXXVII, No. 4. 1889.
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1 82 H. WILD [vol. it, xo. 3.]
setzte Lage der Magnete der Variationsapparate ergibt bei der iibli-
chen Bezifferung der Scalen, wo die Zahlen vom Beobachter aus von
links nach rechts wachsen, fur zunehmende Scalentheile wachsende
westliche Declination und wachsende Horizontal- und Vertikal-Inten-
sitat an. Bei der Lloyd'schen Wage ist vorausgesetzt, dass gemass
meinen Angaben iiber dem horizontal liegenden Spiegel des Wage-
balken-Magnets ein rechtwinklichtes Glas-Prisma aufgestellt sei,
welches die Bewegnng desselben urn eine horizontale Axe schein-
bar in eine solche urn eine vertikale verwandelt, so dass ebenfalls
an horizon taler Scale wie bei den iibrigen Apparaten zu beobachten
ist und sodann habe ich angenommen, dass dieser Magnet parallel
zutn magnetischen Meridian mit Nordpol nach Nord gewendet
orient irt sei, weil dann Erschiitterungen den Magnet nicht aus die-
ser seiner Lage herausbringen, wie dies geschieht, wenn er senk-
recht oder unter irgend einem Winkel zura Meridian aufgestellt
wird.
Die Scalen-Ablesung kann nach Belieben entweder mittelst
Fernrohren erfolgen oder man kann nach Einsetzung passender
Linsen an Stelle der planparallelen Verschlussglaser der Magnetge-
hause vor den planen Magnet-Spiegeln die Bilder der Scalen /, s
oder Sin a und a' m ttelst Lupen, die Fadenkreuze besitzen, be-
trachten und ablesen. Beim Registrirapparat im Saale / y sollen
ausserdem in a die Lampe und auf der Steinconsole s' s' die drei
Registrir-Trommeln mit dem empfindlichen Papier aufgestellt sein.
Der Beobachter aber an den Instrumenten fur absolute Messungen
in D y I und H kann behufs directer eigener Ablesung der Varia-
tionsapparate im Saale P leicht und rasch zur Ablesestelle in a ge-
langen oder dem dort befindlichen Beobachter zu dem Ende mund-
lich ein Zeichen geben. Die Thermometer der Intensitats-Instru-
mente werden ebenfalls mittelst Fernrohren von den Stellen a und
a aus abgelesen, wobei kleine electrische Gluhlampen mit Hohl-
spiegeln zur Beleuchtung der Scalen sehr zweckdienlich sind.
Bei der Berechnung der Wirkung der Magnet-Combination fur
die Ablenkungs-Beobachtungen in H haben wir endlich vorausge-
setzt, dass beide Magnete, der Hulfsmagnet normal im Meridian
und der Hauptmagnet senkrecht dazu, sich im Punkte H befinden.
Beobachtet man die Intensitat nach der Gauss' schen Vethode, wobei
nur kleine, etwa mit Femrohr und Scale vom Pfeiler in C aus zu
beobachtende Ablenkungen des Hiilfsmagnets erfolgen, so wird das
Resultat unserer Berechnung offenbar nicht merklich verandert,
wenn man zugleich bedenkt, dass bei der in Wirklichkeit excentri-
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OBERIRDISCHES MAGNE T. OBSER I A TORIUM 1 83
schen Lage des Haupt- oder Ablenkungs- Magnets jeweilen die da-
durch veranderte Wirkung auf die Variometer durch die Umkehr
desselben urn 180 im Resultat wieder aufgehoben wird. Dasselbe
gilt auch fur die Modification der Gauss' schen Methode, wo der
Hauptmagnet sowohl bei den Schwingungen als Ablenkungen im
Punkte H bleibt, dagegen bei den letztern der Hiilfsmagnet in der
Verlangerung des transversal gestellten Hauptmagnets rechts und
links von diesem in gewisser Entfernung aufgestellt wird. Auch
die Einwirkung des Declinationsmagnets und sammtlicher Varia-
tionsapparate auf die Intensitat an den excentrisch zu H gelegenen
Stellen des Hiilfsmagnets wird nur um ganz zu vernachlassigende
Grossen anders als bei centrischer Lage des Hulfsniagnets.
Erfolgen dagegen die Messungen der Horizontal-Intensitat in H
mittelst eines magnetischen Theodolithen nach der Lamont'schen
Methode, wo die beiden Magnete bei den Ablenkungen stets auf-
einander senkrecht bleiben, so ist zwar auch hiebei die Einwirkung
der iibrigen Magnete auf den Hiilfsmagnet in seinen sei es centri-
schen, sei es excentrischen Stellungen sowie sein storender Einfluss
auf die Variation sapparate nur ganz unerheblich verschieden von
den oben berechneten, wohl aber hebt sich die storende Einwirkung
des Hauptmagnets in seinen beiden Stellungen Nordpol nach Ost
und Nordpol nach West gewendet auf die Variationsapparate nicht
mehr heraus. Die Rechnung hat mir indessen gezeigt, dass selbst
in dem, fur einen magnetischen Theodolithen jedenfalls als extre-
men zu bezeichnenden Fall, wo ein Hauptmagnet von 90 mm.
Lange und vom magnetischen Moment 2X io 7 (mm., nig., s.) in einer
Entfernung von 360 mm. den Hiilfsmagnet um 32 ° ablenken resp.
aus seiner transversalen Stellung bei den Ablenkungs-Beobachtun-
gen um diesen Betrag herausgedreht wiirde, doch die daraus sich
ergebende Modification des S. 179 angegebenen absoluten Fehlers
unserer Bestimmungen der Horizontal-Intensitat durch die gegen-
dH
seitige Einwirkung der Magnete hochstens- - = 0.0000 160 betragen
also noch erheblich hinter der oben festgesetzten Genauigkeits-
grenze zuriickbleiben wiirde
Nach den Auseinandersetzungen in meinein Artikel : „Ueber
die Bestimmung der erdmagnetischen Inclination und ihrer Varia-
tionen" 1 darf man wohl erwarten, dass in kunftigen magnetischen
Observatorien die normalen absoluten Inclinations- Bestimmung en nur
1 Vierteljahrsschrifl der Naturf. (iesellschaft in Zurich fur 1898, S. 253; sieh
auch diese Zeitschrift Vol. II., S. 90. Sept. 1897.
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184 &• WILD (Vol. IV, No. 3.]
mit Inductions' If iciinator ten werden ausgefiihrt werden. Die Vor-
aussetzung, dass in unserem Gebaude an der Stelle / zu obigem
Zwecke ein Inductions-Inclinatorium sich befinde, wird also nicht
beanstandet werden. Dabei ist es gleichgiiltig, ob man ein Induc-
tions-Inclinatorium benutze, dessen Inductoraxe um gleich grosse
Winkel zur Inclinations-Richtung nach der einen und andern
Seite im magnetischen Meridian geneigt wird, und wo dann nach
der Multiplikations-Methode die beim Hin- und Herdrehen des
Inductors um 180 schliesslich constant werdenden Ausschlage
eines Galvanometer-Magnets beobachtet werden, oder ob man nach
der Null-Methode die Stellung der Drehungsaxe eines Inductors im
magnetischen Meridian aufsuche, wo bei continuirlicher Drehung
desselben unter Benutzung eines Commutators kein Strom mehr
im Galvanometer angezeigt wird. Im einen und andern Fall wird
man ein Galvanometer mit einem astatischen Magnet-Paar benutzen,
so dass die bezugliche Annahme von Seite 170 erfullt sein wird.
Das Declinatorium habe ich als vom Intensitatsapparat resp.
einem magnetischen Theodolithen in H getrennt angenommen, wie
dies z. B. im Observatorium zu Pawlowsk der Fall ist 1 und das be-
treffende besondere Instrument fur die absolute Declinations-Be-
stimmung auf den Pfeiler D verwiesen. Fur eine genaue Messung
dieser Art ist ein vollkommenes Temperatur-Gleichgewicht in und
um das bezugliche Instrument von besonderer Wichtigkeit, was
durch die Nahe eines Beobachters, wie beim Theodolith, nur zu
leicht gestort wird. Auch die iibliche Bestimmungsweise des Azi-
muts der Mire wiirde von der Stelle H aus gewisse Gomplicationen
und Schwierigkeiten bereiten. Ich habe mir daher die Anordnung
der Apparate fur die absolute Declinations- und Inclinationsmes-
sung folgendermassen gedacht.
Auf dem Pfeiler D ist als Declinatorium ein wenig modificirtes
Unifilar-Magnetometer wie in U und W aufgestellt. Der Magnet
desselben wird von einer, etwa 12 mm. weiten und 1 mm. dicken
Stahlrohre gebildet, in deren Innerm der Planspiegel angebracht
ist. Derselbe lasst sich von aussen in seinem fixirbaren Biigel
ohne Oeffnung des Gehauses um 180 umdrehen und leicht durch
einen gleichgeformten, kupfernen Torsionsstab ebenfalls mit Spiegel
im Innern ersetzen. Die kupfernen Dampfer konnen wie beim
Unifilar zu ihrer Probe auf Eisenfreiheit entfernt werden, auch soil
fur den Torsionsstab eine passende Dampfung, etwa durch ein
» Siehe die erwahnte Beschreibung des Observatoriums in Pawlowsk S. 12 und 14,
sowie S. 53-5 6 -
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OBERIRDISCHES MAGNET. OBSERVATORIUM 185
Solenoid mit Starkstrom, vorhanden sein. Der Torsionskreis mit
mikrometrischer Verstellung und Ablesung bis auf 1' ist am untern
Ende der etwa 1.5 m. langen Suspensionsrohre angebracht und ein
Metall-Draht als Aufhangefaden des Magnets benutzt. Mit seinem
nivellirbaren Dreifuss ist das Declinatorium in Rinnen von zwei
senkrecht zum magnetischen Meridian auf der Pfeilerplatte aufge-
kitteten Schienen gestellt, so dass es darauf senkrecht zum Meri-
dian verschoben werden kann. Unterhalb ist in den Pfeiler mit
passender Neigung ein Collimator-Fernrohr eingesetzt.
Das Fernrohr zur Einstellung auf die Normale des Magnetspie-
gels und unter passender Neigung auf das Fadenkreuz des Collima-
tors befindet sich auf dem Pfeiler Lf bei /. Es reprasentirt das
centrische, ungebrochene etwa 60 cm. lange und auf die Unendlich-
keit eingestellte Fernrohr eines Universal-Instruments mit Horizon-
tal- und Vertikalkreis, deren Verniere oder Mikrometer-Mikro-
skope je mindestens 5" direct ablesen lassen. Die Lagerstiitzen der
Horizontalaxe sind so hoch, dass sich das Fernrohr durchschlagen
lasst und man mit demselben bei einer Neigung von 71 zum Hori-
zont immer noch am Horizontal-Kreis vorbei sehen kann. Das
Ocular hat zwischen den Linsen und dem Fadenkreuz nach Gauss
einen durchbrochenen geneigten Spiegel oder besser eine geneigte
dunne Glasplatte zur Beleuchtung des letztern von aussen und am
Objectiv lasst sich ein King mit kleinem geneigten Spiegel auf-
setzen.
Vor dem Pfeiler £/ gegen das Declinatorium bin ist unterhalb
auf einem entsprechend der Inclination des betreffenden Orts abge-
schragten Steinpfeiler der Inductor des Inductions-Inclinatoriums
so befestigt, dass das Fernrohr des Universal-Instruments bei einer
der Inclination gleichen Neigung zum Horizont in die Verlange-
rung der Rotationsaxe des Inductors zu liegen kommt und ein senk-
recht zu dieser Axe am obern Ende derselben befestigter justirba-
rer Planspiegel ein Bild des erleuchteten Fadenkreuzes im Focus des
Objectivs geben kann. 1 Die Inductoraxe ist auf ihrer Unterlage
mit ihrem unteren Ende seitlich und mit dem oberen in ihrer Nei-
gung zur Steinflache justirbar. Das zum Inductions-Inclinatorium
gehorige kleine Galvanometer mit bifilar-aufgehangtem astatischen
Magnetpaar ist, wie schon bemerkt, auf dem Pfeiler G aufgestellt,
so dass die Spitze der Suspensionsrohre unterhalb die Horizontale
1 Eine kurze Beschreibung dieser Vorrichtung mit Inductor habe ich S. 264 des
oben erwahnten Artikels, ( T eber die Bestimmung der magnet. Inclination etc. ge-
geben.
6
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1 86 H* WILD [vol. iv, No. 3 1
durch den Declinations-Magnet und die Horizontalaxe des Univer-
sal! nstruinents zu liegen kommt.
Die Declinations-Messung geschieht in der Art, dass man das
Fernrohr des letztern bei horizontaler Stellung auf den Magnet des
Declinatoriums nach vorheriger Auf hebung der Torsion des Suspen-
sionsdrahtes richtet und so lange um die Vertikalaxe dreht bis das
Fadenkreuz und sein Spiegelbild im Magnetspiegel sich decken,
darauf dasselbe wiederholt, nachdem der Magnet um i8o° in seiner
Fassung gedreht worden ist. Das Mittel der beiden entsprechen-
den Ablesungen am Horizontalkreis gibt fur diesen den magneti-
schen Meridian an. 1 Um analog die Ablesung fur den astronomi-
schen Meridian zu finden, visirt man mit dem Fernrohr durch eine,
mit planparallelen Glasplatten verschlossene, die beiden Wande des
Gebaudes durchsetzende Rohre //' hindurch das Fadenkreuz des
gleich hohen, ebenfalls auf die Unendlichkeit eingestellten Fern-
rohrs eines astronomischen Theodolithen an, der ausserhalb des
Gebaudes auf dem Steinpfeiler A aufgestellt und dort hochstens
von einer leichten, zu offnenden oder ganz zur Seite zu schiebenden
Holzhutte zum Schutz vor den Unbilden der Witterung umgeben
ist. Behufs Erzielung der Coincidenz beider Fadenkreuze sind
das erste Mai zwei Beobachter nothig. Mit dem Instrument in A
ist dann schliesslich durch Beobachtung des Polarsterns die dem
astronomischen Meridian zukommende Ablesung an seinem Hori-
zontalkreis zu bestimmen, die durch Uebertragung auch die ent-
sprechende am Horizontalkreis auf D' liefert. Der Collimator im
Steinpfeiler D t dessen Azimut nach den vorigen Messungen unmit-
telbar zu ermitteln ist, gestattet, ihn im Intervall zwischen solchen
vollstandigen directen Bestimmungen als Mire zu benutzen. Diese
Methode bietet die Moglichkeit dar, die Vortheile eines gleichmas-
sig temperirten Raumes fur das Declinatorium m:t denen der
Beobachtung im Freien fur die Azimutbestimmung zu vereinigen.
Ein eventueller prismatischer Fehler der Glasplatten / und /' kann
selbstverstandlich durch Umdrehen der Rohre um i8o° oder Ent-
fernen der Glasplatten zu Zeiten gleicher Temperatur innen und
aussen ermittelt und eine bezugliche Correction daraus abgeleitet
werden.
Die ermittelte Ablesung am Horizontalkreis des Universals auf
1 Die saculare Aenderung der magnetischen Declination, im mittleren Europa
ungefahr i° in io Jahren, erfordert eine allmahliche Verschiebung des Declinatoriums
zur Seite (68 mm. in io Jahren), wenn die optische Fernrohraxe in D 1 und die Magnet-
axe in D centrisch bleiben sollen ; daher die oben erwahnte Aufstellung des Declina-
toriums auf Schienen.
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OBERIRDISCHES MAGNET. OBSERVATORIUM 187
dem Pfeiler D % welche dem magnetischen Meridian entspricht, er-
laubt nun auch, die Inductoraxe in diesen Meridian zu bringen ;
man hat einfach das untere Lager seitlich mit den Justirungsschrau-
ben so lange zu verschieben, bis der Spiegel am obern Ende dessel-
ben eine Coincidenz des Vertikalfadensdesdarauf gerichteten Fern-
rohrs mit seinem Spiegelbild ergibt; hebt und senkt man dann das
obere Lager der Axe, bis diese Coincidenz auch bezuglich des Hori-
zontalfadens eintritt, so ist im Meridian die optische Axe des Fern-
rohrs parallel der Inductoraxe und diese endlich auch parallel der
Inclinationsrichtung, wenn bei der Drehung des Inductors kein
Strom mehr inducirt wird resp. die Galvanometernadel in G ruhig
bleibt. Die Bewegungen aber der letzteren werden an ihrem Spie-
gel vermittelst des erwahnten kleinen Spiegels vor dem Fernrohr-
Objectiv, der nur einen Theil des Gesichtsfeldes verdeckt, zugleich
mit dem Bild des Fadenkreuzes vom Inductor-Spiegel beobachtet,
was die Operation der Justirung sehr erleichtert. Wahrend bei
jeder Inclinationsbestimmung die Justirung der Inductoraxe im
Meridian bis zur Strom-Annullirung zu erfolgen hat, wo dann die
Ablesung am Vertikalkreis als Differenz gegen den Horizontalpunkt
— dieser wird durch Drehung um 180 um die Vertikalaxe und
Durchschlagen des Fernrohrs bestimmt — die Inclination ergiebt,
braucht man dagegen die Justirung derselben parallel zum Meri-
dian nur nach langeren Zeitintervallen auszufiihren, da ja bekannt-
lich eine Aenderung dieses Azimuts um o°.5 fur die Inclination nur
einen Fehler von einigen Secunden bedingt.
Nachdem ich hiemit die Instrumente und ihre Aufstellung in-
soweit erortert habe, als es zur Realisirung ihrer Unterbringung in
demselben Gebaude ohne Risiko einer gegenseitigen Stoning und
Beeintrachtigung ihrer Functionen nothig war, kann ich jetzt zu
einer naheren Beschreibung des Gebaudes, seiner Construction und
der zweckentsprechenden Temperirung und Ventilation seiner
Raume iibergehen.
Das eigentliche, die Sale P und P r mit ihrem Zwischenraum um-
schliessende Gebaude hat eine kreuzfbrmige Gestalt (Tafel VI,
Fig. 1) und ist an beiden Enden des langeren Schenkels von Vorzim-
mern h k und h' k' flankirt, die als Entries dienen. Ohne letztere ist
das Gebaude 16 m. lang und 8 m. breit, abgesehen von dem noch 2.5
m. vorstehenden mittleren Kreuzarm, und ist vom umgebenden Erd-
boden bis zur Dachfirst (Tafel VI, Fig. 2) 6.2 m. hoch. Von der 0.3
bis 0.4 m. dicken Aussenwand stehen die einfachen, 0.1 m. dicken
Holzwande der Sale rings um 0.7 bis 0.8 m. ab und ebenso ist
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iSS H. MILD [Vol. IV, No. 3.]
auch die Decke dieser Sale (sieh die punktirten Linien in Tafel II)
von der Innenseite des ausseren Daches durch einen entsprechen-
den Luftraum getrennt, so dass die aus dem Luftheizungsofen V
und V bei 4, 5 und /, 5' austretende erwannte Lult nieht bloss
ringsum in den Corridoren c und c\ sondern auch iin Zwischen-
raum zwischen den beiden Dachern die Sale umspiihlen kann. Die
Corridore erhalten dureh die niedrigen Doppel-Fenster /,, f t% f\
und/' 2 in der Aussenwand Licht, ausserdem hat diese Aussenwand
nur noch bei T und T' doppelte Fliigelthiiren, eine innere Glas-
thiir und eine aussere massive Thiire, welche aber fur gewohnlich
geschlossen bleiben. Ihnen entsprechen an den Wanden des mitt-
leren Saales die Fliigelthiiren 6 und 6\ die aber bis auf spater zu
besprechende Oeffnungen fur gewohnlich auch geschlossen sind. so
dass dieser Mittel-Saal nur durch die drei, mit punktirten Linien
angedeuteten Laternen iiber den Pfeilern D y I und H Licht em-
pfangt, wahrend die beiden seitlichen Sale P und P' ganz dunkel
sind. Wie man sieht werden sie von den durchgehenden Wanden
des Mittel-Saals noch ausserdem durch zweite Holzwande, die
einen Zwischen-Corridor von 1 m. Breite abgrenzen, getrennt. An
den Enden dieses Corridors gegeu den ausseren befinden sich die
eigentlichen Eingangsthiiren f v / r // und // zu den Salen und zum
Mittelraum, zu welchem Ende die Thiiren r p r v r\ und r\ sowie
9v ?r 9 1 un d g t in den Zwischen wanden angebracht sind. Vor der
nordlichen Thiire T ist eine bis nahe in's Niveau des Corridor-
und Zimmerfussbodens erhohte Plattform Q angedeutet, auf wel-
cher bei A der Steinpfeiler fur den astronomischen Theodolithen
vor der Visir-Rohre / /' steht, und ebenso sind da die seitlichen
Schutzwande fur diesen Pfeiler und das Instrument darauf scizzirt
sowie die nach aussen (Norden) sich offnende, bis zum Dach rei-
chende Fliigelthiire. Selbstverstandlich kann der Zweck der Azi-
mutbestimmung fiir das Instrument auf dem Pfeiler D' auch noch
in anderer Weise z. B. durch eine vom Hauptgebaude ganz isolirte
Aufstellung des Theodolithen auf einem Pfeiler in der Verlange-
rung der Linie D' A erreicht werden, wo dann die Schutzhutte
fur die Beobachtung ganz zur Seite geschoben werden konnte.
Sammtliche Steinpfeiler und so auch A sind vom umgebenden
Fussboden isolirt wie es in Tafel VI, Fig. 2, fiir einen mittleren
Pfeiler dargestellt ist.
Die Vorzimmer mit den Eingangen bei e und e haben einen
doppelten Zweck. Der erste Raum h und h' mit seitlichem Fenster
ist zum Heizen der Ofen V uud V und zur Aufbewahrung des
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OBERIRDISCHES MAGNET. OBSERVATORIUM 189
unmittelbar nothigen Heizmaterials und der Reinigungs-Utensilien
bestimmt, wahrend der zweite abgetrennte, ebenfalls mit Fenster
versehene Raum k und k' fiir die Beobachter als Ablegezimmer
vor dem Einlritt in die Corridore und Beobachtungsraume die-
nen soil.
Die Benutzung der Raume geschieht namlich in folgender
Weise. Zu den Vorzimmern h und h' haben sowohl die Beobachter
als Diener (Heizer) Zutritt durch die von aussen mit besondern
Schlusseln, von innen mit zuriickziehbaren Riegeln zu offnenden
Thiiren m und m' . Zu den ahnlichen Schlossern der Thiiren n
und //' der Ablegezimmer sowie den Corridorthiiren o und o' haben
nur die Beobachter Schliissel, so dass ohne ihre Gegenwart die
Diener nicht zu den inneren Raumen gelangen konnen. Der de-
jourirende Beobachter tritt also durch o resp. 0' in die betreffenden
-Corridore ein und von da durch die mit automatischen Schliessern
versehenen Thiiren / 2 resp. t\ in die Zwischen-Corridore, aus denen
sie dann durch die Thiiren q % resp. q\ in die Sale P resp. P' zur
Ablesung der Variometer fiir directe Beobachtung resp. zur Bedie-
nung des Magnetographen gelangen. Da hiebei die Thiiren r v r 2 ,
r f x und r\ zum mittleren Saal fur gewohnlich verschlossen sind und
nur die alteren Beobachter fiir die absoluten Messungeu zu ihnen
Schliissel besitzen, so kann der Beobachter, der z. B. zuerst den
Saal P von e her betreten hat, ohne aussen herumgehen zu miis-
sen, durch die Thure t t und den Corridor an T' vorbei zur Thiire
/', und damit zum Saale P' gelangen. Durch die Thiiren t x und t\
kann der Beobachter auch den nordlichen Corridor c und c' betre-
ten, um sie zu untersuchen und eventuell die Klappen der Luft-
heizungsofen bei 4 und 4' zu reguliren, wie er dies beim Eintritt
auch in 5 und 5 ' thun kann.
Zum Mittel-Saal haben, wie schon angedeutet, bloss die vorge-
riickten Beobachter, denen die absoluten Messungen iibertragen
sind, freien Zutritt und zwar auch aus den Zwischen-Corridoren
durch die Thiiren r. Nur bei der absoluten Declinationsmessung
werden auch die Thiiren 6 und T im Sommer voriibergehend ge-
offnet, wenn der astronomische Meridian fiir das Instrument in //
mit Hiilfe dessen in A bestimmt werden soil. Ausserdem haben
sie wie die in 6' und T' den Zweck, grossere Instrumente und Ge-
genstande bequemer in die Sale bringen zu konnen und bei Feuers-
gefahr eine rasche Evacuirung der Sale zu ermoglichen. Dass die
Beobachter fiir gewohnlich stets die Heizzimmer h und h' zu passi-
ren haben, soil die Deponirung von magnetischen Gegenstanden
durch die Diener in diesen Raumen verhiiten.
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190 H. WILD [Vol. IV, No. 3]
Die Beheizung der Sale ist zur Venneidung rascher Tempera-
turwechsel in der Art regulirt, dass die unter dem Fussboden der
Heizzimmer durchgefiihrten Kanale 2 und j, J und j Aussenluft
den Kammern der Luftheizungsofen V und V zufiihren, welche
nach der Erwarmung daselbst durch die Klappen ^ bis j' in die
Corridore c und c' stromt und diese nach Angabe der Pfeile durch-
fliesst, um bei 6 und 6' durch die vergitterten grossen Klappen in
den Thiiren daselbst in den Mittel-Saal einzutreten, aus dem sie
dann wieder durch entsprechende Klappen in den Thiiren r, bis /,
in die Zwischen-Corridore und von diesen durch Klappen in den
Thiiren q x bis q\ in die Sale P und P' gelaugt, welche sie endlich
bei den Klappen 9, 10 , 9' und io r am untern Ende der Ventilations-
schornsteine verlasst. Diese liegen beiderseits vom Rauchkamin
der Verbrennungsraume V und V\ denen durch die mittleren Ka-
nale / und /' Luft von aussen zugefiihrt wird. Wie man sieht, ist
zur Venneidung directer Erwarmung der Sale vom Ofen aus der
letztere von der Saalwand durch einen Luftzwischenraum getrennt.
Will man den einen oder andern Saal /^und P' mit den Varia-
tions-Instrumenten fur sich oder auch gemeinsam mit dem Mittel-
Saal behufs Bestimmung der Tempera tur-Coefficienten starker als
die andern erwarmen oder durch Nicht-Beheizung abkiihlen, so
werden z. B. die Thiiren /, und /, des ersten Zwischen-Corridors so
geoffnet, dass sie durch Anlehnen an die gegeniiberstehende Ecke
des Corridors diesen weiterhin ganz abschliessen. Alsdann kann
die durch c und c' vom Ofen V herbeistromende Luft nur in diesen
Zwischen-Corridor eintreten und, da zugleich die Klappen der Thii-
ren r, und r t geschlossen worden sind, bloss durch q x und q t in den
Saal P stromen. Selbstverstandlich ist hiebei in den Corridoren
auch nach oben zu ein Abschluss iiber den Thiiren t x und /, und
ebenso iiber der Scheidewand gegen den Mittel-Saal hin nothwen-
dig. Der letztere und der Saal P' behalten ihre normale Beheizung
oder konnen bei dieser Combination, wahrend P normal beheizt
wird, zusammen erwarmt oder abgekiihlt werden. Analog verfahrt
man mit P\ wenn dieser Saal fur sich erwarmt oder abgekiihlt wer-
den soil.
Beziiglich des Baumaterials ist vor Allem zu bemerken, dass
dasselbe durchaus eisenfrei resp. unmagnetisch sein soil und dass
deshalb auch Materialien, welche gewohnlich als eisenfrei betrach-
tet werden, wie z. B. weisse Backsteine, Granit, Marmor einer Vor-
priifung auf Eisenfreiheit zu unterwerfen sind. Asbest und Port-
land-Cement, die man fniher als unmagnetisch annahm, sind den
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OBERIRDISCHES MAGNET. OBSERVATORIUM
191
neueren Untersuchungen zufolge ganz zu verwerfen. Als gewohn-
lich eisenfreies Baumaterial konnen wir bezeichnen : Holz verschie-
dener Art, Sagespahne, Kohlenpulver, Schwefel, Glas, Thon, reiner
Quarz und Quarzsand, weisser bis grauer Marmor, weisser Kalk-
stein, heller Gran it, Gneiss, heller Sandstein, Alabaster-Gyps, weisse
Backsteine und Thonplatten, Filz, Dachpappe, Kupfer, Messing mit
Reserve.
Welche von diesen Materialien zu empfehlen und in welcher
Dicke fur die Wande z. B. dieselben anzuwenden seien, hangt we-
sentlich von den Anforderungen ab, welche an die Temperirung
der Raume gestellt werden. Nach den Erorterungen in meinem
Eingangs erwahnten Artikel dieses Journals ist das Mindeste, was
wir in dieser Beziehung zu verlangen haben, dass die tagliche Tem-
peratur-Oscillation in den Salen nicht mehr als o.°i betrage. Will
man auch fur das Jahr eine moglichst constante Temperatur an-
streben, so wird man immerhin eine Variations-Amplitude von i°
(Differenz von Max. und Min.) zulassen miissen. Um eventuell
unter naturlichen Verhaltnissen d. h. ohne Beheizung eine solche
Temperatur-Constanz zu erzielen, hat man gewohnlich bloss auf die
Leitungsfahigkeit der Substanz der Wande etc. Rucksicht genom-
men. Nun hangen aber wie im Erdboden so auch bei Gebauden
die Effecte der eindringenden Warmewellen durchaus nicht bloss
von der Leitungsfahigkeit allein, sondern vielmehr vom Quotien-
ten derselben durch die sogen. Warmecapacit'at d. h. die zur Erwar-
mung der Volumseinheit des betreffenden Korpers um i° nothige
Zahl von Calorien ab. Heissen wir diese Grosse C, so ist :
C = c. s
wenn s das specifische Gewicht und c die specifische Warme der
Substanz darstellt und die Wdrmeconstante K ist dann
'■4
wenn k das Leitungsvermogen oder die Leitungsfahigkeit reprasen-
tirt. Diese Warmeconstante regiert alle Warmeverhaltnisse, auf die
es hier ankommt. Wollen wir z. B. wissen, in welchem Verhalt-
niss eine gewisse innerhalb eines Zeitintervalls T sich manifesti-
rende Temperaturvariation A an der Oberflache eine;s Korpers bei
der Fortpflanzung in's Innere desselben bis zu einer Tiefe p sich
vermindere oder wie gross die Temperaturvariation [\p in dieser
Tiefe noch sei, so besteht nach Fourier und Poisson die Gleichung :
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192
H. WILD
[Vol. IV, No. 3]
wo log. e der log. vulg. der Basis e des naturlichen Logarithmen-
Systems darstellt und die Coustante A'allein massgebend ist. Be-
zogen auf Centimeter und Minute als Langen- und Zeit-Eiuheit hat
man z. B. fur
C k K Autor.
Tannenholz quer zur Faser . . 0.34
Coniprimirte Sftgespahne . . . 0.34
Tannenholz langs aer Faser . 0.34
Eichenholz quer zur Faser . . 0.54
Hartgummi (Ebon it) 0.28
Steinkohle 0.30
Eichenholz langs der Faser . . 0.54
Gyps (Stuck) 0.70
Schnee von mittl. Dichte 0.20 . 0.10
Glas 0.46
Gemeiner Thon 0.47
Sand und Thon, trocken ) 0^^.0.44
Thon, feucht j lBoden o45
Sand-Boden 0.30
Marmor, weiss und feinkornig 0.57
Feldspathstein aus Japan . . .0.57
Gran it, grobkornig 0.52
Sandstein 0.50
Sandsteinboden 0.46
Luft 0.00031
Kupfer 0.78
Soil also z. B. eine oberflachliche Tages-Amplitude der Tempe-
ratur von 30 auf eine solche von o.°i und eine Jahres- Amplitude
der Tages-Mittel von 20 auf eine solche von i.°o reducirt werden,
so erhalten wir nach der obigen Formel fur verschiedene Werthe
von K folgende zugehorende Tiefen p y wenn man fur T im erstern
Fall 1440 Minuten und im zweiten Fall 365.25 X 1440 Minuten
einsetzt und die gefundenen Centimeter in Meter verwandelt :
0.006
0.018
Forbes.
0.007
0.021
Forbes.
0.018
0.053
Forbes.
0.029
0.053
Lees & Neumann.
0.016
0.056
Stefan.
0.020
0.068
Neumann.
0058
0.106
Lees & Neumann.
0.078
0.1 1 1
Herschel, Ledebour &
0.016
0.160
Abels. [Dunn.
0.094
0.204
Stefan.
0.098
0.210
Lees & Neumann.
0.150
0.339
Angstrom.
0.157
0.354
Angstrom.
0.157
0.523
Forbes.
0.315
0.554
Lees & Neumann.
0.353
0617
Ayrton & Perrey.
0.335
0.645
Neumann.
0.400
0.800
Neumann.
0.641
1.386
Forbes.
0.0047
15.4
Stefan.
60.5
77.5
Neumann & Angstrom*
T
= 24*
T= 1 Jahr.
K
P
fur
A.
-r— 300
m
p fiir — °= 20
m
0.03
0.2I
2.1
0.06
O.3O
3-o
O.30
O.67
6.7
0.60
0.95
95
1. 00
1.22
12.2
Es wiirde hiernach eine aus Tannenholzbalken dicht gefugte
Wand oder eine zwischen Holzbretter festgestampfte Schicht von
Sagespahnen von 0.2 m. Dicke und eine solche aus Eichenholz
quer zur Faser genommen oder aus Tannenholz langs der Faser
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OBERIRDISCHES MAGNET. OBSERVATORIUM I93 ,
oder aus Steinkohle (Kohlenpulver zwischen Holzwanden) von
0.3 m. Dicke geniigen, urn die Tagesperiode der Lufttemperatur
auch in extremen Fallen fur das Innere bereits auf o.°i zu reduci-
ren. Denselben Effect wiirde eine Lehm-Wand von 0.6 bis 0.7 m,
Dicke haben, wahrend Marmor (Kalkstein) und Granit bereits eine
Wand-Dicke von 0.9 bis 1.0 m. und Sandstein gar eine solche von
1.2 m. zu dem Ende erfordern wurden.
Die Jahresperiode der Temperatur in mittleren Breiten wiirde
zur Verminderung auf i° durchweg 10 Male grossere Wand-Dicken
verlangen.
Das gilt nun aber alles bloss unter der Voraussetzung, dass
Wande und Decke ein ringsum geschlossenes Ganze bilden und
keinerlei Communication zwischen dem Innern- und der Aussen-
luft stattfinden wiirde. Durch Fenster und Thiiren selbst in ge-
schlossenem Zustande und durch die nothwendige, wenn auch be-
schrankte Ventilation wird aber stets ein gewisser Austausch der
Luft aussen und im Gedaude stattfinden, welcher die obige theoreti-
sche Temperatur-Constanz im Laufe des Tages resp. des Jahres be-
eintrachtigen wird. Wenn indessen der Beobachter, wie in unserem
Fall, drei Thiiren zu passiren hat, ehe er in die Corridore gelangt,
und die Fenster auf ein Minimum reducirt werden, so ist der Tem-
peratur-Effect des Luftaustausches auf die Wande und andere feste
Gegenstande im Innern in Anbetracht des Umstandes ein geringer,
dass ja die Warmecapacitat der Luft 1000 Male kleiner ist als die der
letztern Korper. Ueberdies gelangt die einstromende Luft nicht
unmittelbar in die Sale, sondern hat jeweilen vorher in den Corri-
doren noch einen langern oder kiirzern Weg zuriickzulegen, was
einen gewissen Ausgleich der Temperatur zur Folge hat. Kann das
Gebaude electrisch beleuchtet werden, so konnen die Fenster/ in
den Corridoren ganz fortfallen und man hat dann nur auf die drei
Laternen im Mittel-Saal die grosste Sorgfalt bei der Construction
zu verwenden, d. h. mindestens drei, durch Luftzwischenraume ge-
trennte, ganz dicht schliessende und dicke Glasplattendacher hinter-
einander anzubringen und die Seiten-Wande der Laternen ebenso
dick wie die Gebaude-Wande zu machen. Die electrische Beleuch-
tung hat aber noch den weitern Vortheil, dass gegeniiber Gas,
Acetylen oder Potroleum eine viel schwachere innere Warmequelle
bei Beleuchtung der Scalen der Variationsapparate und fur die
photographische Registrirung derselben sich manifestirt und auch
die Feuersgefahr eine geringere wird. Als Material fur die innern
Corridorwande empfiehlt sich, ein solches von hoher Warmecapaci-
7
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194 H- WILD [Vol. IV, No. 3]
tat zu wahlen, das in Folge davoti hauptsachlich regulirend auf
Temperatur-Variationen im Corridor einwirkt, also z. B. Eichen-
holz oder Stuck (Gyps).
Nach dem Allem diirfte es also wohl moglich sein, die Tages-
periode der aussern Lufttemperatur bis zur angegebenen Grenze
von o.°i durch massig dicke aussere Wande bei unserem Gebaude
fur die Sale zu eliminiren, ohne zu einer eigentlichen Beheizung
der Raume zu schreiten, dagegen wird man in mittleren Breiten
eine solche nicht wohl umgehen konnen, um im Laufe des Jahres die
erwahnte Temperatur-Constanz von ± o.°5 zu erzielen. Angenom-
men selbst, man wollte zu dem Ende 2 — 3 m. dicke Wande aus Holz,
oder 6 — 7 m. dicke Lehmwande errichten, so wiirde sich im Innern
ohne Beheizung eine das Jahrestnittel der Lufttemperatur um 1 — 2
iibersteigende mittlere Temperatur herstellen, also z. B. in Mailand
15 — 16 , in Paris 12 — 13 , in Berlin 9 — io°, in Petersburg
4 — 5 . Die letzteren Tempera turen waren nun fur den Aufent-
halt der Beobachter in diesen Raumen nicht eben zutraglich, alle
wiirden aber fur die betreffenden Orte im Sommer haufig erheblich
unter der Thaupunktstemperatur der freien Luft liegen, so dass
diese beim Eindringen in die Sale eine Condensation ihres Wasser-
dampfes erfahren, jedenfalls aber die relative Feuchtigkeit der Luft
daselbst bedenklich erhohen wiirde. Es ist also jedenfalls eine
Beheizung des Gebaudes, ganz abgesehen von der Erleichterung
zur Bestimmung der Temperatur-Coefficienten der Instrumente, zu
ermoglichen. Nach den Erfahrungen im Observatorium zu Paw-
lowsk muss dann als constante Temperatur des Gebaudes eine
solche von mindestens 20 C. gewahlt werden, wenn man ohne wei-
tere Vorkehrungen wahrend des Sommers ein Ansteigen der Feuch-
tigkeit in den Salen bis zu 90 Procent, was fur die Instrumente be-
reits schadlich ist, vermeiden will. Ist die Moglichkeit vorhanden,
die aussere Luft vor dem Eintritt in das Gebaude durch Eiskeller
oder lange und tiefliegende unterirdische Ranale zu leiten, so kann
wohl die constante Temperatur etwas niedriger genommen werden.
Jedenfalls aber hat zu dem Ende, da die Tagesmittel der Luft-
Temperatur in mittleren Breiten selten iiber 20 steigen, fast das
ganze Jahr eine Beheizung des Gebaudes zu erfolgen, so dass man
auch die obigen exorbitanten Anforderungen an die Dicke der
Wande kann fallen lassen. Zur Regulirung der Beheizung wiirde
es sich in diesem Fall eher empfehlen, an eine Aussenwand von
Tannenholz und 2 — 3 Decimeter Dicke (zur Beseitigung der tag-
lichen Temperaturvariation) eine innere Bekleidung oder Wand
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OBERIRDISCHES MAGNET. OBSERVATORIUM 195
von gleicher Dicke aber aus einem Material von hoher Warmeca-
pacitat anzuschliessen, also etwa von Stuck, Marmor oder gutem
Kalkstein.
Diese Complicationen alle werden aber ohne wesentlichen Scha-
den fur die Genauigkeit der Beobachtungen umgangen, wenn man
bloss fur 24 Stunden eine Tempera turconstanz bis o.°i verlangt, im
Laufe des Jahres aber dem Tagesmittel der aussern Lufttempera-
tur mit der Gebaude-Temperatur nachfolgt, wobei man allerdings
die letztere, damit die Gegenwart des Beobachters das Temperatur-
Gleichgewicht nicht zu sehr store, nicht erheblich unter 15 C. sollte
sinken lassen. Alsdann hat man im Sommer von der Feuchtigkeit
ohne Weiteres nichts zu fiirchten und man braucht zur Erfiillung
der letztern Bedingung in mittleren Breiten nur im Winter-Halb-
jahr, ahnlich wie in unsern Wohnungen, zu heizen.
Diesen Erwagungen gemass schlage ich fur das Gebaude eine
massive Aussenwand nebst Dach aus Tannenholz von 0.3 m. Dicke
vor innen und aussen mit gut zusammengefiigten Brettern bekleidet
oder in Ermanglung von Balken zwischen diesen Brettern eine
festgestampfte Sagespahne-Schicht gleicher Dicke oder dann, wenn
am Ort Holz nicht gut zu beschaffen ware, eine 0.6 m. dicke Lehm-
Schicht. Nur die beiden Vorzimmer und ihre Scheidewand gegen
die Corridore hin, wareu der Feuergefahrlichkeit halber wie die
beiden Ofen aus weissen eisenfreien Backsteinen aufzufuhren. Die
mit asphaltirter Dachpappe gedeckten Dacher sollten ebenso wie
die Aussenwande des Gebaudes zur Verminderung der Einstrahlung
weiss gestrichen werden. Die Saal-Wande sind aus starken Eichen-
brettern in doppelter Lage mit abwechselnden Fugen sorgfaltig
dicht herzustellen und aussen und innen gut zu firnissiren, so dass
auf lange Zeit jede Reparatur, die fur die gute Function der In-
strumente so storend ist, unnothig wird. — Die massiven Holz-
thiiren <?,V, T'und 7' sind iiberdies zu wattiren und sehr dicht-
schliessend zu machen, die ausseren Glasfenster/mit einem weissen
durchscheinenden Ueberzug zu versehen und ebenso auch die
obersten Glasscheiben der Laternen. Die Thiiren 6, 6\ r und q
haben alle in ihren unteren Hal ft en grosse, mindestens 0.5 m. in*s
Quadrat haltende vergitterte Oeffnungen, welche eventuell mit
Holzklappen dicht zu verschliessen sind. Sammtliche Steinpfeiler
sind aus hellem Marmor oder Sandstein hergestellt und stehen
frei auf einem, 1 m. tiefen Fundament aus eisenfreiem Kalkstein.
Auch der Sandsteinsockel der Wande von 0.5 m. Hohe iiber dem
umgebenden Terrain steht auf entsprechendem Kalkstein- Funda-
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196 H. WILD [Vol. IV, No. 3.)
ment; trockener, festgestampfter reiner Sand bildet zwischen dem
Sandsteinsockel die Unterlage (eventuell mit Asphaltschicht da-
zwischen) fur den ohne Cement aus Thonplatten zusammengefug-
ten Fussboden der Sale und Corridore. Der Fussboden soil keine
Zeichnungen, sondern eine uniforme helle Farbung haben, um auf
ihn herunterfallende kleine Gegenstande, wie Schrauben, leichter
finden zu konnen. Filzplatten schliessen oben den Zwischenraum
zwischen den Pfeilern und dem Fussboden ab.
Nach den Erfahrungen im Observatorium zu Pawlowsk kann ich
nicht genug empfehlen electrische Beleuchtung auch da anzuwen-
den, wo dieselbe nicht von aussen her fertig zu beziehen ist. Da
Lampchen von 6 Volt einfach oder zu mehreren combinirt vollkom-
men fiir den vorliegenden Zweck geniigen, so ist eine beziigliche
besondere Einrichtung im entfernten Hauptgebaude der Anstalt
mit Petroleummotor, kleiner Dynamomaschine und 12 Accumulato-
ren, je zu drei abwechselnd functionirend vollkommen ausreichend
und leicht zu beschaffen und zu unterhalten. Es konnen dann die
Fenster in den Corridoren, ja eventuell sogar die Laternen im Mit-
telsaal, ganz fortfallen und ausserdem ist eine geringere Ventila-
tion der Raume nothig.
Fiir die Beheizung habe ich ebenfalls zufolge den beziiglichen
giinstigen Erfahrungen im Observatorium zu Pawlowsk, undzwarso-
wohl im steinernen Variations-Gebaude als im holzernen Pavilion fiir
absolute Messungen daselbst, steinerne Luftheizungsofen angenom-
men, welche zugleich die nothwendige Ventilation bei sehr gleich-
massiger Erwarmung der Luft ermoglichen. Nicht die Beschaffen-
heit der Wande und Decken der Sale und des Gebaudes sind es
namlich, welche die Hauptschwierigkeit fiir die Erhaltung constanter
Temperatur in den Salen darbieten, sondern die im Allgcmeinen
nicht zu umgehende Beheizung der Raume und die nothwendige
Ventilation derselben. Ofen, welche rasch viel Warme liefern und
sich auch rasch wieder abkiihlen, sind deshalb trotz der die Warme-
vertheilung regulirenden Corridore durchaus zu vermeiden, und
ebenso konnen besondere Ventilations- Vorrichtungen leicht starkere
Temperatur- Variationen bewirken. Mit unsern Luftheizungsofen
ist zur Vermeidung solcher Storungen des Temperatur-Gleichge-
wichts in den Salen etwa in folgender Weise zu operiren. Im
Herbst ist mit der eigentlichen Beheizung zu beginnen sowie die
Temperatur in den Salen zufolge den drei Male taglich von den Be-
obachtern auszufiihrenden Ablesungen der Thermometer anfangt
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OBERIRDISCHES MAGNET. OBSERVATORIUM i 97
unter 15 herunter zu gehen. Der Vergleich dieses Sinkens der
Temperatur mit dem mehr oder weniger beschleunigten Sinken des
Tagesmittels der Luft-Temperatur im Freien giebt dem Beobachter
nach kurzer Uebung die Mittel an die Hand, dem Heizer das jewei-
len zu verbrennende Quantum Holz oder Kohle anzugeben, das zur
Compensation jenes Sinkens der Temperatur nothwendig ist. Da-
bei wird immer nur Abends nach Sonnenuntergang angeheizt, um
dem nachtlichen Temperatur-Minimum bereits entgegenzuarbeiten.
Sollte es bei sehr starken plotzlichen Temperaturerniedrigungen im
Winter gemass dem erwahnten Vergleich der Aussen- und Innen-
Temperatur durch die Beobachter geboten sein, so kann selbstver-
standlich auch wohl am Tage einmal geheizt werden und umge-
kehrt konnen die Warmeklappen durch die Beobachter zeit-
weise geschlossen werden, wenn in dieser Jahreszeit plotzliche
starke Erwarmungen eintreten. Es ist die mit der Heizung gleich-
zeitig verbundene starke Ventilation, welche diese Vorsicht nothig
macht. Doch ist es bei der langsamen Wirkung der Luftheizungs-
ofen und der Regulirung durch die Corridore durchaus nicht
schwer, in den Salen die Temperatur im Laufe von 24 Stunden um
nicht mehr als o.°i variiren zu lassen. Im Friihjahr nimmt mit
abnehmender Starke der Beheizung auch die automatische Ventila-
tion der Raume ab und wiirde mit Aulhoren des Heizens ebenfalls
fast Null werden. Es ist daher gerathen, auch in der Jahreszeit,
wo das Tagesmittel der Luft-Temperatur iiber 14 — 15 betragt,
doch jeweilen am spaten Abend den Luftheizungsofen ganz wenig
anzuheizen, um in der Nacht eine schwache Ventilation zu unter-
halten, welche das Temperatur-Gleichgewicht im Innern wegen der
Abkiihlung der aussern Luft zu dieser Tageszeit nicht merklich
stort.
Selbstverstandlich diirfen im Winter die Thiiren T f und T
nicht geoffnet werden. Zur Beobachtung des Azimuts in A ist
jener Raum von aussen zuganglich.
Die beiden Heizraume h und h! sollten durchaus mit Feuer-
krahnen und Spritzenschlauchen versehen sein, um bei Feuersgefahr
sogleich Wasser in geniigender Menge zur Hand zu haben; man
wird dann auch in k und U Wasserhahne anbringen und, wenn es
wiinschenswerth erscheint, in dem einen oder andern dieser Ablege-
zimmer ein kleines photographisches Laboratorium einrichten
konnen.
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198 H. WILD [Vol. iv, No. 3]
Wie ich in meinem friiheren Artikel bereits erwahnt habe, wa-
ren allfallige besondere Untersuchungen mit andern Instrumenten
zur Controle und Verbesserung der Beobachtungsmethoden, Ver-
gleichung mit Instrumenten anderer Anstalten und Uebungs-Be-
obachtungen zweckmassig in einem andern ebenfalls eisenfreien
Gebaude auszufuhren.
Zurich, 27. Juni 1899.
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THE INFLUENCE OF THE EARTH UPON THE FIELD OF
A BAR-MAGNET.
By W. W. Griffith.
Where the lines of force about a bar-magnet are determined
experimentally under the influence of the earth's field, either by
filings or by a short tracing needle, all the curves about the ends of
the magnet will be seen to be concave toward the extended axis,
when the A' seeking pole of the magnet points north. Also, the
end curves will all be seen to be open curves for all horizontal posi-
tions of the magnet except when the N seeking pole points south.
For all positions of the magnet the curves as shown by the filings
will be seen to be very different from those shown by the tracing
needle. The azimuth of the magnet very materially affects the
curvature of the lines, and particularly so when the lines are traced
by a short needle. The curves traced by a floating needle are very
different from those shown by the filings or by the tracing needle.
The following experiments were made with the object of testing
the above statements :
Figures i to 6 inclusive are photographs of lines of force traced about
a bar-magnet by means of a short magnetic needle. The bar-magnet was
15 cm. long, and capable of sustaining from one end a weight of 55 gm. of
soft iron. The tracing needle was 1.5 cm. long. Every line in the original
drawings from which the photographs were taken, was traced in the ordinary
way by actual experiment, the drawings being 65 by 50 cm.
In Fig. 1 the N seeking pole points north. This figure shows that all the
lines of force about the ends of the magnet pass off to infinity, and that they
are concave towards the axis produced of the magnet, and that the lines be-
tween the poles are closed curves, part of the circuit being made through the
magnet. Four neutral points are indicated by small circles. The arrows in-
dicate the direction in which the needle points.
In Fig. 2 the S pole of the bar- magnet points north. In this case all the
tracings are closed curves. If, however, a curve at some distance from the
magnet is traced, as the outside curve in the figure t the curve may possibly
pass off to infinity. For example, if the tracing needle is made to approach
cor (/, on the outer curve, from the S pole of the bar-magnet it may pass off
to infinity at these two neutral points, c or c / . If the curve is traced from
the N pole the two neutral points will be symmetrically placed at the upper
end of the figure.
In Fig. 3 the Af pole of the bar-magnet points east The figure produced
is askew, as it should be ; for the earth lines will deflect the lines as traced
about the N and 5 poles of the bar to the left and right, respectively.
199
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200
U r . W. GRIFFITH
Fig. i. — A* seeking pole of magnet Fig. 2. — A* seeking pole of magnet
points north. points south.
-4v ;
Fig. 3. — A* seeking pole of magnet Fig. 4. — X seeking pole of magnet
points east points west
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FIELD OF A BAR-MAGNET
20 1
! I I
• , '. • ; ; t \ 1 x \ : > ;•
■'M \ \ \\\\i I I I I I,
nil
X X
Fig. 5. — A' seeking pole of magnet
points towards the zenith.
Fig. 6. — S seeking pole of magnet
points towards the zenith.
Fig. 7. — N seeking pole of magnet
points north.
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202 W. W. GRIFFITH
In Fig. 4 the N pole of the bar-magnet points west. This is also askew,
and is a mirror image of Pig. 4.
In Fig. 5 the N pole of the magnet points towards the zenith, while in
Fig. 6 the S pole points towards the zenith. In both cases the lines radiate
from the poles in curved lines.
Fig. 7 represents the lines of force about a bar-magnet, as shown by
filings, the photograph being taken from a large field, with the N seeking
pole of the magnet pointing uorth. The magnet is the same as the one used
in Figs. 1 to 6.
The lines as traced by the filings correspond to those traced by
the tracing needle in Fig. 1, except that in Fig. 7 the radii of curv-
ature of the lines are much greater. However, in Fig. 7 the lines
about the ends of the magnet are plainly concave toward the axi»
produced, and pass off to infinity.
It might be anticipated that the lines from the filings would be
of greater curvature than those from the needle. In Fig. 1 the
tracing needle is a permanent magnet in all positions relative
to the bar-magnet, while in Fig. 7 the little particles of filings
as magnets are only temporary' magnets by induction, and be-
come weaker as they recede from the bar-magnet. This will
cause the horizontal pull, or directive force of the earth lines, to
become less and less the farther the filing-magnet is away from the
bar-magnet ; hence, the lines about the ends, as shown by filings,
will be more nearly straight lines than in Fig. 1. In Figs. 5 and
6 the lines are very much curved, while the lines, if shown by
filings, would appear to be straight lines. It is obvious, then, that
if a tracing needle be held in various positions over the field repre-
sented by filings, the needle would not be tangent to the curves as
shown by the filings.
Experiment will show that a floating needle being free to move
under the influence of a bar-magnet in the earth's field will not de-
scribe curves similar to those described by filings or by a tracing
needle. The floating needle will acquire a certain amount of ki-
netic energy at every successive position relative to the bar-magnet,
which is cumulative all along the curve, and will produce a curve
different from that from the filings or from the tracing needle, even
though all the lines be traced in an isolated field.
University of Missouri, Columbia, Mo., June 5, 1899.
Department of Physic9.
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' PROFESSOR GEORG B. NEUMAYER.
Professor Georg Balthasar Neumayer, a recent photograph (1898) of
whom we have the pleasure of reproducing in our present number, was
born in Kirchheim-Bolanden, Bavaria, on June 21, 1826. He studied in
the Gymnasium and Lyceum in Speyer from 1842 to 1845, and acted as
assistant to Professor Schwerd, the well known physicist and author of
the famous work "Die Beugungserscheinungen." In 1847 and 1849 he
passed the examinations as student in the Technical High School of Mu-
nich. In 1850 and 1855-56 he worked in Munich with Lamont, the noted
magnetician. From 1850 to 1854 he went to sea, and passed the exami-
nation as master of navigation.
In 1859 he established at Melbourne the Flagstaff Observatory, de-
voted to the study of terrestrial magnetism and physical science in gen-
eral. He continued as director of it until 1864. From 1858 to 1864 he
carried out the magnetic survey of the Colony of Victoria. On his re-
turn to Germany he was engaged on the computation, discussion, and
publication of the meteorological and magnetic observations made in
Australia. This work was done at the expense of the British Govern-
ment. In 1872 he entered the Kaiserliche Admiralitat in Berlin as the
first hydrographer of that office.
He was elected director of the newly-founded Deutsche Seewarte in
March, 1876, by decree of Emperor William I. This position he holds
at the present time. In certain respects the " Seewarte " has no equal
in the world.
Professor Neumayer's great services to terrestial magnetism are too
well known to require elaborate mention. It need only be instanced that
all of the investigations made in recent years pertaining to the analysis
of the earth's permanent magnetic field have been based upon his ex-
cellent magnetic maps of 1885. It is not generally known, however, that
magnetic work forms no part of the regular scheme of the Deutsche
Seewarte, and that hence Professor Neumayer's extended labors in this
direction have been carried on entirely during his leisure hours when
freed from official duties. This bespeaks the man's great devotion to his
favorite work. He has also found time to encourage and stimulate others
in their investigations, and in some instances has furnished the financial
means himself.
We rejoice with Professor Neumayer that his long-cherished project
of antarctic research, for which he has so eloquently and so persistently
pleaded, has at last met with realization.
Professor Neumayer is the author of many valuable scientific papers,
and is an influential member of several important scientific associations.
He is to preside this year over the meeting of the " Deutsche Natur-
forscher und Aerzte," to be held in Munich, in September.
203
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NOTES
ACTIVITY IN MAGNETIC WORK.
Notice to Workers in the Fields of Terrestrial Magnetism and Atmos-
pheric Electricity. — It would add greatly to the interest and value of these
pages if those who are engaged in magnetic or electric work would give
prompt notice to the Editor of the kind and character of the investiga-
tion to be undertaken. A few lines on a postal card is all that is required.
The Editor is glad to receive at any time items of current interest, no
matter what their length may be. Remuneration is made for all such
items at the end of the year. By attending to this matter, our co-workers
could assist us greatly in adding to the attractiveness of the Journal.
Professor IV. von Bezold, at the meeting of the Berlin Academy,
June 15th, read a paper entitled: " Ueber die Sonnenstrahlung in der
Atmosphare und das Polarlicht." An abstract will appear in the next
issue.
The following items of interest have been kindly sent us by Professor
Eschenhagen :
"Dr. van Rijckevorsel has made, during June of the present year, an-
other series of comparisons at Kew and Potsdam between his instruments
and the observatory standard instruments.
"Dr. Edler y of Potsdam, is engaged in magnetic work in the eastern
part of West Prussia. He is making the attempt to operate at the same
time a small temporary magnetic observatory at Marienburg, West
Prussia. The instruments consist of the self-registering transportable
Eschenhagen magnetometers, to be described in the next number. They
are placed in a cellar, and the value of the zero-line is determined by
the usual method.
"Professor Birkeland (Christiania) has undertaken an expedition to
Bossekop. He is provided with the necessary instruments for making
magnetic observations. In his outfit is one of Eschenhagen's transport-
able self-registering magnetometers.
"Professor Adam Paulsen (Copenhagen) is planning a trip to Iceland
for the purpose of studying the phenomena of the polar lights and of the
earth's magnetism.
" For similar purposes to those of Professor Paulsen, a Swede-Russian
expedition will set out for Spitzbergen and northern Norway"
204
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NOTES
205
We are indebted to Signor Rajna for copies of the " Perse veranza,"
published at Milan, of May 8th and 17th. In the first issue, Signor
Rajna, in an extremely interesting article, entitled " La trazione elettrica
e gli osservatorii magnetici," discusses, among other things, the perni-
cious effect of electric-tramway currents upon magnetic observatories,
and deplores the fact that Italy is not adequately supplied with mag-
netic equipments.
In the second issue, Signor Fracastoro calls attention to the magnetic
work done at the Technical Institute of Verona, which possesses a
complete magnetic outfit after Wild's designs.
Professor Alexander McAdie, who is now Forecast Official at the
Weather Bureau, San Francisco, has been appointed Honorary Lecturer
on Meteorology in connection with the Berkeley Astronomical Depart-
ment of the University of California.
Dr. L. A. Bauer will leave Washington for Europe early in September,
on business for the Coast and Geodetic Survey, and is to be away about
three months. He will inspect various magnetic observatories, and
compare the Coast and Geodetic Survey instruments with observatory
standards. He will also attend the Seventh 7 International Geographical
Congress, to be held in Berlin, as delegate from the National Geographic
Society of Washington.
Manuscripts received during the Editor's absence abroad will receive
prompt attention. The next number of the Journal will doubtless
appear by the end of December.
Mr. Daniel L. Hazard, a member of the Computing Division of the
Coast and Geodetic Survey since 1892, has been transferred to the Divis-
ion of Terrestrial Magnetism. Mr. Hazard, during the past seven years,
has made the magnetic computations, and has shown exceptional skill in
the intricate least square adjustments arising in geodetic work. He
takes charge .of the office work in terrestrial magnetism during Mr.
Bauer's absence in the field.
Messrs. /. A. Fleming and H. W. Vehrenkamp, who graduated this
year at the University of Cincinnati, having successfully passed the civil
service examination for Aid in the Coast and Geodetic Survey, have been
assigned to the Division of Terrestrial Magnetism.
Mr. Vehrenkamp, after making some magnetic observations in the
vicinity of Washington for determining a suitable site for the Coast
Survey Magnetic Observatory, proceeded to Indiana, where he is now
engaged upon a magnetic survey of that State.
Mr. Fleming has completed his magnetic observations in Delaware,
and in September entered upon a magnetic trip west of the Mississippi.
Messrs. Putnam, Farris, and Ritter, who are engaged in geodetic
work in Alaska, have been supplied with magnetic instruments, so that
magnetic data may be obtained in this region.
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ABSTRACTS AND REVIEWS
INFLUENCE OF ELECTRICITY ON THE GROWTH OF PLANTS. 1
In this interesting paper, read before the British Association for the
Advancement of Science, the author presents in detail as the causes leading
to the investigations the following: :. The adaptation of needle-like leaves of
fir-trees and beards of cereals to act in the capacity of transmitters of elec-
tricity from the air to the earth. 2. The periodicity of particular and other-
wise unexplainable variations of the year-rings of fir-trees from different
latitudes, which is in full agreement with the periods of the sun-spots and
the auroras, being more pronounced as the latitude increases. 3. The period-
icity of the harvest results in Finland, which agrees with the periodical vari-
ations in the sun-spots, and in the number of polar lights. The conclusion
being that the active factor is atmospheric electricity, the following experi-
ments were made. After a short history of previous work in this line, there
follows an exhibit of the results obtained from experiments made in southern
Finland and Bourgoyne. The method employed consisted essentially in
carrying on, at the same time, like cultivations in two fields, conditions being as
nearly equal as possible, save that a wire net connected to the positive pole of
a machine of the Holtz or Wimshurst type was spread over the one, and the
electricity forced to flow from points of the net into the air. The conclu-
sions, seemingly well taken, from a great number of results are: 1. The elec-
tricity given to the air through points in connection with the one pole of an
electric machine, the other being conducted to the earth, exercises under all
circumstances a great effect on growing vegetables. 2. The effect will be
greatly favorable to the development of the vegetables only when the supply
of water is, within certain limits, barely sufficient. 3. This will be the case,
for the most part, of vegetables under ordinary circumstances, assuming that
the electricity is given during three or four hours in the morning, and three
or four hours in the afternoon, avoiding the hours of highest sun, when the
sky is clear. 4. When the supply of water is abundant, the electricity can be
given during the whole twenty-four hours with a favorable result 5. The
surest way to produce a favorable effect seems to be to limit the giving of the
electricity to a moderate time y so that the vegetative process is not forced too
fast The paper is concluded by a discussion of some of the probable causes
of the effect of the electricity, together with a promise of further and more
perfected investigations covering a greater territory. J. A. Filming.
Semmola: Atmospheric Potential. The author discusses the influence
of earth-air electric currents and of those traversing the rarefied strata of the
atmosphere, causing a decrease of potential with the altitude.
Nuova Cimento, March ; abstracted briefly in Lond. Elec. June 23d, and
Elect. W. & Eng., July 22d.
SOUTH POLAR LIGHTS.'
In Dr. Bollers's first memoir on the southern auroras, which was published
in the earlier part of the third volume of Gerland's Beit rage, he treated of the
chronological and geographical distribution of the aurora australis, although
the want of abundant material led to some unsatisfactory results. Since that
1 Lemstrom, Selim, Professor of Physics at University of Helsingfors: " Experi-
ments on the Influence of Electricity on Growing Vegetables or Plants:' Repr.
from " Electrical Review," Nov. 24 and 25, Dec. 2 and 16, '98.
*Boller, W. Das Sudlicht. Zweite Abhandlung. Gerland's Beitrage zur Geo-
physik, Band III, Leipsic, 1898, pp. 550-609.
206
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REVIEWS
207
time the author has most diligently continued the search for data, examining
not only the printed books in continental and British libraries, but numerous
collections of manuscripts and a large number of daily and weekly periodicals.
Although the results of this search have brought to light a far larger material
than could have been supposed to exist, and although his publications will
doubtless stimulate future observers to more careful auroral records, yet, in
general, this increase of material is not likely to change the conclusion ex-
pressed by him in his first memoir to the effect that before the year 1840 the
aurora australis was actually as frequently and as fully developed as the aurora
borealis, but was not observed or recorded, owing to the general lack of inter-
est in the subject by those living in the southern hemisphere. He finds that
it is a phenomenon as regular in the southern hemisphere as in the northern.
The data recently discovered by him do not change the general character of
the annual and other periodicities given in his previous memoir. The sun-spot
period is marked with great clearness. The total number of dates of auroras
Catalogued by Boiler is 791. The annual maxima occur in March and Octo-
ber, the minima in November and June.
The sun-spot period is shown by the following annual sums, in which we
begin with 1840, because the records previous to the establishment of the
magnetic observatories at Hobart Town, St. Helena, Cape Town, Mauritius,
Auckland, etc., are too fragmentary :
1840
18
1850
i860
42
1870
58
1880
6
1890
7
1841
22
1851
5
1861
16
1871
62
1881
11
1891
6
1842
22
1852
1
1862
7
1872
40
1882
39
1892
45
1843
7
1853
1863
11
1873
7
1883
28
1893
22
1844
2
1854
1
1864
5
1874
37
1884
2
1894
2[
1845
13
1855
1865
3
1875
13
1885
9
1895
3
1846
1
1856
3
1866
2
1876
3
1886
13
1896
1
1847
11
1857
6
1867
1877
3
1887
8
—
1848
9
1858
22
1868
1878
2
1888
13
—
1849
1859
36
1869
4
1879
2
1889
7
—
By far the greater number of these were observed in Australia, New Zea-
land, and Tasmania. None were recorded in Cape Town, Natal, or South
America. This distribution agrees with the conclusion that the zone of
maximum frequency is no more symmetrical about the geographical South
Pole than it is about the North Pole. Its location was determined in Boiler's
previous memoir. Assuming that the auroral streamers emanate from this
zone, Boiler revises his previous computation of the altitude of the auroral
light and obtains 80 kilometers for auroras observed at Melbourne and 130
kilometers for those observed on the southern border of the Australian con-
tinent The complete copy of auroral records appended to Boiler's article
seems to make it unnecessary for the student to refer to the original sources,
and greatly lightens the labors of future investigators. We thus owe Dr.
Boiler a debt of gratitude for his exhaustive search for auroral records.
U. S. Weather Bureau. Cleveland Abbe.
RECENT PAPERS ON ATMOSPHERIC ELECTRICITY.
At the meeting of the Vienna Academy of Sciences of March 9th, Profes-
sor Exner presented three papers upon atmospheric electricity. For the
following abstracts we are indebted to the Naturwissenschaftliche Rundschau,
July 8th :
I. Hans Bensdorf : Measurements of Falls of Potential in Siberia.
The author reports concerning the measurements of atmospheric electric-
ity in Siberia carried out by him under the auspices of the Vienna Academy.
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208 RE VIE WS [VOU IV, No. 3 J
Since no measurements of atmospheric potential have been made in those re-
gions when the humidity of the air is less than 2 mm. vapor pressure, it ap-
peared of particular interest to determine how potential fall is related to
moisture of the air, by making measurements of atmospheric electricity
during winter in Siberia.
As the most favorable place for these experiments, Tomsk 1 was chosen,
where the author spent the months of January and February, 1898. In con-
sequence of unfavorable weather, complete observations could be carried out
only upon twelve days. From nearly 260 single measurements, an average
fall of potential of 145 volts per meter was obtained, the highest observed
value being 310 v/m.
The temperature fluctuated between — o°-5 and — o°-45 C, and the vapor
pressure fluctuated between o. 1 and 4 mm. For a determination of the daily
period, none of the observed data sufficed ; still a pronounced maximum at 2
o'clock P. M. was clearly shown.
II. Josbp Thcma: Measurements of Atmospheric Electricity in a
Balloon.
The author has carried out, partly, at the cost of the Vienna Academy,
seven balloon trips for the purpose of making measurements of atmospheric
electricity. The plans followed embraced first an investigation of the distri-
bution of the electrical charge of the atmosphere during clear weather;
and second, the investigation as to whether a balloon, during its flight, is
electrically charged. While the first question has a purely scientific significa-
tion, the second is important scientifically as well as practically. Scientifically,
because the measurements of the electro-static fall of potential at different
heights above the earth would, of course, be vitiated by the electric charge of
the balloon. The practical importance of the second question has made itself
prominent of late years through the repeated burning of balloons, the cause
being assigned to electric sparks.
The author, after reviewing the previous work of Exner, discusses the re-
sults of his seven balloon trips, and reaches the following conclusions: 1. The
positive fall of potential decreases with increasing height ; there are, there-
fore, accumulated positive charges in the lower strata of the atmosphere.
2. An electric charging of the balloon could not be detected in the last
four trips.
III. Rud. Ludwig : On the Measurements of Atmospheric Electricity
made during the Total Eclipse of the Sun, January 22, 1898.
The purpose of this investigation was to determine whether the passage
of the shadow-cone through the. air had an influence on the normal fall of
potential. According to the theory of Arrhenius, and also according to the
photo-electric theory, such should be the case and should mauifest itself in
an increase of the fall of potential. The observations which were made in
South India under favorable meteorological conditions show a distinct dim-
inution of the fall during and immediately after totality of the eclipse, fol-
lowed by an increase until the normal value was reached. To what cause
this change of potential is to be assigned, remains at present unexplained.
J. A. F.
1 = 56° 30' N., X ~ 84 58' E. ; height above sea level = 134 m.
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REVIEWS
209
Niesten, L. Bulletin mensuel du magnHisme terrestre de V Observatoire
Royal de Belgique. Bruxelles, 1899. 13 x 18 cm.
In response to a wish expressed at various times, the Royal Observatory
of Belgium, situated at Uccle, near Brussels, began this year the publication
of a monthly r£sum£ of the magnetic observations made at the Observatory.
These monthly bulletins will be given again in a collected form, at the end of
the year, in the "Annuaire" of the Observatory. Thus far three of these inter-
esting bulletins, January, February, and March, have reached us. In the
*' Introduction" to the January number, the necessary data for the proper
understanding of the tables are given. In Tables I, II, and III, the readings of
declination, horizontal and vertical inteusity, as obtained from the Adie Mag-
netograph, are given for every day in the month at the hours, o, 6a, noon, and
6p, also the daily and monthly means, the maximum and minimum values
with the corresponding times, the diurnal ranges, daily character of the traces
and, in the column of remarks, the aspect of the solar disk. Table IV gives
the daily departures from the monthly mean.
Following the tables is a review of the magnetic phenomena of the month,
and on appended plates the traces of some unusual occurrences are reproduced.
The " Bulletin " is prepared by MM. Niesten and Prinz. L. A. Bauer.
Magnetic Effects Produced by Lightning. — In No. 8 of the series of
Frammenti concemanti la geofiscia (Rome), Dr. Folgheraiter gives an in-
teresting account of the singular magnetic effects produced by lightning
on a house at Terre Nuova, which was struck on April 8th last. The ob-
servations led the author to conclude (1) that the lightning produced a
large number of singular points and zones in the masonry, it being in-
admissible that the individual stones should have been so highly mag-
netized before construction of the walls; (2) that while doubts have
hitherto existed as to the possible formation of singular points in tufa,
this question has now been answered in the affirmative ; (3) the alternation
in the polarities of the singular points and zones, even on the same piece
of tufa, is noteworthy, but no connection has yet been established be-
tween these alternations and the mode of propagation of the electricity;
(4) it is now amply proved that lightning produces marked magnetiza-
tion independently of the inductive action of terrestrial magnetism. 1
" Disturbing Effects of Electric Tramways on Magnetic Needles" by
Signor Marini. — The author made researches in Rome for the purpose of
ascertaining the causes of the disturbances. The measurements were
carried out by a Wiedemann galvanometer without coils, thus reducing
it to a simple magnetometer. Three causes were found: A direct influ-
ence of the current in the overhead line and in the rails, noticeable to
a distance of not over 150 m.; an influence of the return currents
wandering through the soil to a distance of 2,000 m. ; an influence
of the iron parts of the motor cars, noticeable for not more than 50 m.
Some diagrams and tables are given.'
1 From Nature, July 27, 1899.
*From the Electrical World and Engineer, July 29th.
. 9
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RECENT PUBLICATIONS
Bezold, W. von. Ueber Erdmagnetismus. Repr. from " Zeitschrift des Verei-
nes deutscher Ingenieure." Bd. XLIII. Berlin, 1899. Pp. 8. 24x31 cm.
[An illustrated lecture delivered before the German Association of Engi-
neers. The author gives a r£sum£ of the principal results of magnetic in-
vestigations, describes the self-registering instruments at Potsdam, exhibits
traces of disturbed and undisturbed days, shows by a diagram the simi-
larity in the curves representing the occurrences of Polar lights, magnetic
disturbances and sun spots for the period 1 784-1 871, discusses the
disturbances from electric tramways as observed at places near Berlin,
and closes his interesting address with an eloquent appeal for the proper
protection of magnetic observatories from such disturbing iufluences.
Magneticians owe a debt of gratitude to Professors von Bezold and
Riicker for the efforts they are making towards the accomplishment of
this desired end.]
. Ueber die Zunahme der Blitzgefahr wahrend der letzten sechzig
Jahre. Sitzb. Berlin Akad. XVI, 1899, pp. 291-300. [The author shows
graphically a connection between the sun-spot curve and the curves show-
ing the relative danger from lightning for the period 1835 to 1897. The
author's previous surmise that a maximum in the sun-spot curve corre-
sponds to a minimum in the lightning curve is again confirmed.]
Borgbn, C. Untersuchungen iiber den Einfluss des magnetischen Moments
und der Entfernung auf die Poldistanz von Magneten. Pp. 36.
British Association Committee, Report of, on Comparing and Reducing
Magnetic Observations. Bristol meeting, 1898.
I. Magnetic Results at Greenwich and Kew discussed and compared,
1889- 1896. By William Ellis. [See next issue.]
II. Account of the late Prof. John Couch Adams's determinations of the
Gaussion magnetic constants. By Prof. W. G. Adams.
Dahlbom, Th. Ueber magnetische Erzlagerstatten und deren Untersuchung
durch magnetische Messungen. Tr. from the Sweedish by P. TJhlich,
Freiberg, Saxony, 1899. 64 pp. 1 PI. Price, 2.50 M.
Doberck, W. Report of the Director of the Observatory for 1898. Hong-
kong Observatory, March 1899. App. B. Magnetic observations made
during the year 1898, comparison of magnetometers and means of 15
years' magnetic observations made in Hongkong.
Duff, Wilmer A. The dip of the magnetic needle in New Brunswick. Read
Dec. 6, '98. Repr. from Bull, of the Natural History Society of New
Brunswick. No. XVII. 1899. 15x22 cm. [The following observations
were made " with a very accurate portable dipping-needle, made by Elliott
Bros, of London." Dip in Aug., '98: At St. John (Fort Howe), 74 35'; St.
Andrews, 74 57'; Oak Point (St John River), 75°Q3 / ; The Point (Bellisle
Bay), 75° 1 5 7 ; Fredericton, 75° 44'; Indian Village (above Fredericton),
210
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RECENT PUBLICATIONS 21 1
75° 5°'- The author not being aware of any previous determinations in
New Brunswick, his attention is herewith called to the following obser-
vations taken from App. I, Coast and Geod. S. Rep. for '97 :
Station. Latitude. Longitude. Date. Dip. Observer.
St John 45 14' 66°o3 / W. 1847.5 75°o6' Prof. G.W. Keely.
S^^to.) 45 <* 67 ° 5 l859 76 °*4 G ' W ' Dean »
( l nang bta.) Qct ^^ ^.^ Q and G s
Eschenhagen, M. Ueber erdmagnetische Intensitatsvariometer. Repr.
from Verhandl. der Deutsche n Physikal. Gesellsch. I Jhrg. Nr. 9.
Pp. 6. 15x23 cm. [See next issue.]
. Ueber die Bedeutung magnetischer Beobachtungen im Ballon.
Abs. by Th. Arendt. Repr. from ZS. fur Luftschiffahrt und Physik d.
Atmosphare, Nr. 9, 10. Sept-Oct, 1898. Pp.6. 17x25 cm. [See Dec. No.]
In No. 8 of the "Frammenti Concernenti La Geofisica dei Pressi di Roma,'*
the following three articles appear :
Folgheraitbr, G. Intensita orizzontale del magnetismo terrestre
a Campo di Grove nell ' Abruzzo. [Cf. p. 209.]
. Singolari effetti prodotti da una fulminazione. Pp. 17-20.
Keller, Filippo. Intensity orizzontale del magnetismo terrestre
presso Carsoli ed Orte. Pp. 1-10.
Fritsche, H. Die Elemente des Erdmagnetismus fur die Epochen 1600,
1650, 1700, 1780, 1842 und 1885, und ihre sacularen Aenderungen, berech-
uet mit Hiilfe der aus alien brauchbaren Beobachtungen abgeleiteten
Coefficienten der Gaussischen "Allgemeinen Theorie des Erdmagnetis-
mus." St Petersburg, 1899. [The less said about this publication the
better. The author in all seriousness undertakes the tremendous labor
of computing the Gaussian coefficients and the magnetic distribution for
the epochs named in the title, under the following assumptions: The
total intensity between 1780 and mean epoch of 1862 and 1885, has
remained unchanged. With the aid of dips and declinations for 1780, he
then determines the coefficients and the distribution for 1780. Next he
assumes the horizontal intensities in 1700 are practically the same as
those derived from the 1780 computations, those for 1650 the same as for
1700, and finally those for 1600 the same as those for 1650. And with
conclusions reached from such heterogeneous computations he ventures
to criticise the results of others! The author poses throughout his
paper as the only true exponent of Gauss. — I*. A. B.]
Hepites, St. C. Elements magn6tiques de Bucarest. Extras din Analele
Institutulul Meterologic al Romaniei, Vol. XIII, 1897. Bucharest, 1898.
Pp- 135— 1 58. 23 x 32 cm.
. Contributiuni la Fisica Globului IV. Determin&ri magnetice in
Rom&nia a. Anul., 1898. Extras din Analele Academiei Rom&ne, Vol.
XX, Series, II, Memoriile Sectiunii Sciiutifice, Bucharest, 1899. Pp. 28.
21 x 27 cm. [See next issue.]
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2 1 2 RECENT PUR LIC A TIONS [Vol. iv, No. 3.]
Lemstrom, S. On the earth-currents and the electrical currents in the atmos-
phere and their relations to the earth-magnetism. Luminous phenom-
ena, natural and artificial, of the nature of the Polar light. "Oefversigt
af Finska. Vet-Soc. Forhandlingar. B. XLI." Helsingfors, 1899. Pp.
45. 14 x22 cm. [See next issue.]
Ludeung, G. Ueber die tagliche Variation des Erdmagnetismus an Polar-
stationen. Sitzb. Berlin Acad., XXXVI, 1898 ; pp. 524-531. [See Dec No.]
. Ueber den taglichen Gang der erdmagnetischen Stdrungen an
Polarstationen. Sitz. Berlin Acad., XIV, 1899; pp. 236-247. One plate.
McAdik, A., and Henry, A. J. Lightning, and the Electricity of the Air. In
two parts. Bull. No. 26; Weather Bureau, Washington, 1899. Price 50
cents. [Part I deals with the electrification of the atmosphere and the
best methods of protecting life and property from lightning stroke, being
in large part a revision of Bulletin No. 15, Protection from Lightning, the
edition of which is about exhausted. Part II gives statistics of actual
losses of life and property, including live stock in the fields, sustained in
the United States during 1898. The aim of the paper is to furnish infor-
mation of practical value to all persons, especially those who have occa-
sion to seek protection from lightning.] Pp. 112. 16 x 23 cm.
Moureaux, Th. R6sum6 des Observations Magn6tiques faites a l'Observa-
toire du Pare Saint-Maur, pendant 15 annees, de 1883 & 1897. Pp. 92.
25 x 32 cm. [Abstract in December issue.]
Murat, I. St. Observatoire Magn6tique de Tlnstitut M6teorologique de
Roumanie & Bucarest Analele Institutului Meteorologic al Rom&niei,
Vol. XIII, 1897. Pp. 8. PI. 1. 23 x 32 cm. [See next issue.]
Palazzo, Luigi. Confronti degli strumenti magnetici italiani con quelli
degli osservatori di Pare Saint-Maur e di Kew. Rome, 1899. Repr.
Rendic. Accad. d. Lincei, cl. d. scienze fisiche, Vol. VIII, ser. 5a.
19 x 27 cm. [See next issue.]
Rijckevorsel, Dr. von. On the analogy of some irregularities in the yearly
range of meteorological and magnetic phenomena. Repr. from Phil.
Mag., Jan., 1899. Pp. 57-66. One plate.
Schwalbb, G. Mittheilungen iiber die jahrliche Periode der erdmagneti-
schen Kraft Met. Z. S. Dec, 1898. Pp. 449-462. [A preliminary com-
munication of the results of the author's interesting investigation regard-
ing the annual variation of the earth's magnetic force. In the present
paper only the magnetic observations at Potsdam, Pawlousk, and Batavia
are utilized. The principal result reached is, that the cause of the annual
period may be referred to electric currents outside of the earth's crust.
We trust that the author will be able to give us soon an exhaustive inves-
tigation regarding this important subject. In the July issue of the same
journal the author makes a few revisions.]
Stonyhurst College Observatory. Results of meteorological and magnetical
observations, with report and notes of the Director, Rev. W. Sidgreaves,
S. J., 1898. Clitheroe, 1899. Pp.80. 12 x18 cm. [Pp. 42-50 contain the
results of the magnetic observations, absolute and differential, and dates
of magnetic disturbances.]
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THE NEW YORK
PUBLIC LIBRARY
A8TOR, LENOX AND
TILDEN FOUNDATIONS.
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[Plate VII]
N <
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Terrestrial Magnetism
and
Atmospheric Electricity
volume iv DECEMBER, 1899 number 4
UBER DIE EXISTENZ ELECTRISCHER IONEN IN DER
ATMOSPHARE.
Von J. Elster und H. Geitei,.
Die Erfahrungen der letzten Jahrzehnte haben zu einer be-
stimmten Vorstellung von der Art der Electricitatsleitung in den
Gasen gefiihrt. Ein Gasmolekiil selbst ist hiernach unfahig eine
electrische Ladung anzunehmen und daher auch nicht im Stande
eine solche zu iibertragen, dagegen kann es durch gewisse Einwir-
kungen in zwei Teile zerlegt werden, deren einer eine unverander-
liche positive, deren anderer die complementare negative mit sich
fuhrt, Ladungen, die enorm viel hoher sind, als diejenigen, die den
betreffenden Teilchen durch Beriihrung mit electrisch geladenen
Korpern mitgeteilt werden konnten. Diese entgegengesetzt gela-
denen Bestandteile des Molekiiles entsprechen also den Vehikeln
<ies electrischen Stromes bei der Electrolyse, man hat deshalb auf
sie dieselbe Bezeichnung " Ionen" angewandt. Es ist gut, sich zu
vergegenwartigen, dass — mindestens fiir elementare oder gar ein-
atomige Gase — wahrscheinlich aber auch allgemein der Sinn
dieses Ausdrucks mit dem fiir Electrolyte giiltigen sich nicht vol-
lig decken kann. Man hat sich hiernach einen electrischen Strom
in einem Gase dadurch gebildet zu denken, dass diese Ionen, die
in dem isolierenden Medium der unzerlegten Molekiile zerstreut
sind, in der Richtung der Kraftlinien des Feldes sich bewegen, die
negativen gegen den positiven und die positiven gegen den nega-
tiven Pol hin. Treffen sie auf Leiter, so geben sie ihre Laduug an
<iiese ab. Nach Analogie des electrolytischen Vorganges hat man
anzunehmen, dass bei der Entladung die Ionen sich wieder zu
neutralen Molekiilen zusammenschliessen, wobei auch sekundare
Reactionen an den Electroden eintreten konnen.
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2i 4 •/• ULSTER UMD H. GEITEL [Vol. iv, No 4 -j
Bei den disruptiven Entladungen in Gasen werden die far den
Electricitatstransport erforderlichen Ionen durch eine Spaltung der
Molekiile in Folge der electrischen Krafte des Feldes selbst gebil-
det, bei der stillen Entladung miissen sie schon vorhanden sein ;
das electrische Feld hat allein die Wirkung, sie in Bewegung zu
setzen. Zu diesen letzgenannten Vorgangen gehort die Electrici-
tatsleitung durch erhitzte oder in chemischer Thatigkeit begriffene
Gase ; in neuerer Zeit ist man besonders auf die Leitfahigkeit auf-
merksam geworden, die durch die Rontgen- oder Becquerelstrahlen
in einem Gase hervorgerufen wird. Man denkt sich die Erschei-
nung in der Weise, dass die durch das Gas absorbierte Energie der
Strahlen zur Auflosung eines Teils seiner Molekiile in Ionen, zur
Ionisierung des Gases, verwandt wird.
Es is ersichtlich, dass die angedeutete Auffassung von den
electrischen Vorgangen in einem Gase von Einfluss sein muss auf
das Bild, das wir uns von den Erscheinungen der atmospharischen
Electricitat machen. Giebt man zu, dass die atmospharische Luft
in dem genannten Sinne in gewissem Betrage ionisiert ist, so han-
delt es sich bei den auf diesem Gebiete auftretenden Erscheinun-
gen nur um die Kenntniss der Bedingungen, unter denen eine
Trennung und Bewegung jener schon praexistierenden Ionen er-
folgen kann. Eine vollzogene Trennung der entgegengesetzt ge-
ladenen Ionen bedeutet eine electrische Potentialdifferenz, eine
Bewegung, einen electrischen Strom.
Um die fur diese Auffassung notige Grundlage zu gewinnen, ist
zunachst festzustellen, ob die atmospharische Luft als teilweis ioni-
siert angesehen werden darf. Die Hauptfrage ist demnach, ob sie
zu einem gewissen Grade die Electricitat leitet, erst wenn diese be-
jaht werden kann, ist zu untersuchen, ob jene Leitfahigkeit der
Hauptsache nach dem Vorhandensein von Ionen zuzuschreiben ist.
Was nun die erstgenannte Frage betrifft, ob die atmospharische
Luft in einigem Maasse die Fahigkeit hat, electrische Ladungen
fortzuleiten (abgesehen von der Art, wie dies erfolgt) so weiss man
schon aus den Versuchen von Coulomb, dass ein von Luft umspiil-
ter electrisch geladener Leiter im Laufe der Zeit seine Ladung all-
mahlig verliert. Wenn hierbei auch ein Teil des Verlusts auf die
mangelhafte Isolation durch die Stiitzen zuriickzufuhren ist, so
kann dieser doch durch Veranderung ihrer Anzahl geschatzt und
soweit in Rechnung gezogen werden, dass der Verlust durch die
Luft allein als sicher erwiesen gelten muss. Messungen dieser Art
an abgeschlossenen Mengen von Luft und andern Gasen liegen in
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ELECTRISCHE ION EN IN DER ATMOSPHERE
215
grosser Sorgfalt von verschiedenen Physikern ausgefiihrt vor.
Hiernach muss man begrenzte kleine Volumina staubfreier Gase bei
gewohnlicher Temperatur und Atmospharendruck als fast absolute
Isolatoren betrachten.
Es is das Verdienst von Herrn Linss 1 die Bedeutung der Elec-
tricitatszerstreuung im freien Luftraume fur die Lehre von der at-
mospharischen Electricitat erkannt und zuerst Messungen des Be-
trags dieser Zerstreuung angestellt zu haben.
Herr Linss bediente sich zu seinen Versuchen eines durch
Schellack isolierten mit Stanniol iiberzogenen Pappcylinders, den
er mit positiver Ladung 5 bis 10 Minuten lang der freien Luft aus-
setzte. 2 Die Messung seines electrischen Potent ialniveaus vor und
nach der Exposition geschah mittelst einer in einem geschlossenen
Gehause aufgehangten iiber einer Teilung schwebenden Magnet-
nadel, die als Sinuselectrometer diente, indem sie durch den gelade-
nen Versuchskorper angezogen wurde. Eine Schatzung des ohne
Beriihrung mit der freien Luft eintretenden Verlusts suchte Herr
Linss dadurch zu erreichen, dass er den Korper in geladenem Zu-
stande die gleiche Zeit im Electrometergehause beliess und wiederum
zu Anfang und Schluss seinen electrischen Zustand bestimmte. Die
Berechnung der in der Zeiteinheit bei constant gedachter Ladung
entwichenen Electricitatsmenge q, ausgedriickt in Bruchteilen der
Anfangsladuug, geschieht nach der Formel :
log K — logV,
q t
in der V und V die Electrometerablesung vor und nach der Ex-
position und / die Dauer der letzteren bedeutet.
Legt man als Zeitmaass die Minute zu Grunde, so ergiebt sich
aus einer zweijahrigen Beobachtungsreihe, dass im Mittel der Elec-
tricitatsverlust des Versuchskorpers in freier Luft nicht weniger als
— seiner urspriinglichen Ladung betrug, d. h. dass bei constant
gehaltenem Potentialniveau in 100 Minuten eine Electricitatsmenge
in die Luft entweicht, die seiner augenblicklichen Ladung gleich
kommt.
Aus diesem Ergebniss zieht Herr Linss mit Recht den Schluss,
dass auch der Erdkorper einen fortwahrenden Electricitatsverlust
an die Atmosphare erleidet, und dass, um diesen zu decken, ihm in
1 W. Linss. Meteorol. Zeitschrift 1887, p. 352 und Electrotechnische Zeitschri/t
1890. Heft 38.
* Fur negative Ladungen erhielt er keinen Unterschied der Zerstreuung.
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216 / ELSTER UND H. GEITEL (Vol. IV, No 4)
100 Minuten durchschnittlich ebensoviel negative Electricitat zuge-
fuhrt werden muss, wie seine Gesamtladung betragt.
Wie bemerkt, ist der angegebene Betrag der Zerstreuung nur
ein Mittelwert, thatsachlich war sie im Laufe des Jahres verander-
lich und zwar im Winter kleiner als im Sommer, auch in den Mor-
genstunden geringer als nach Mittag. Sie wurde nicht vermehrt
bei Zunahme der relativen Feuchtigkeit, auch die Anwesenheit von
Nebel hatte keine Vergrosserung zur Folge. Bei kiihlem Regen-
wetter ging sie auch im Sommer bedeutend zuriick.
Die offen zu Tage liegende Wichtigkeit solcher Messungen hatte
in uns den Wunsch erregt, sie zu wiederholen. Eine Schwierigkeit
lag allein in der Auffindung einer Methode, die keinerlei Bedenken
ausgesetzt ware. Es ist namlich nicht zu leugnen, dass das von
Herrn Linss angewandte Verfahren die Grosse des Verlusts durch
die Schellack isolation nicht ausreichend in Rechnuug zu ziehen er-
laubt. Man kann nicht sicher behaupten, dass dieser in dem ge-
schlossenen Electrometergehause annahernd derselbe ist, wie im
freien, wenn die isolirenden Flachen von der ausseren Luft bespiilt
werden ; der Verdacht liegt nahe, dass er im letzten Falle grosser
sein wird, also auch eine scheinbare Vermehrung des Zerstreuungs-
coeffizienten in freier Luft bewirken kann.
Wenngleich dies Bedenken nach unsern spateren Erfahrungen
eine thatsachliche Grundlage nicht hat, so war es doch von vorn-
herein nicht abzuweisen.
Der zu construierende Apparat 1 muss als wesentlichen Bestand-
teil zuerst einen Korper enthalten, von dessen Oberflache aus die
Electricitatsabgabe an die Luft erfolgen soil und ferner ein Electro-
meter, das zur Beobachtung seines electrischen Zustandes dient.
Damit der durch die unvollkommene Isolation verursachte Fehler
moglichst gering sei, ist die Anzahl der isolierenden Stiitzen soweit
zu beschranken als es die Stabilitat erlaubt, doch ist dabei zu for-
dern, dass man jederzeit von der Grosse dieses Fehlers zuverlassige
Kenntniss erlangen konne. Eine geringe Capacitat des Apparats
ist wiinschenswert, damit ein Electricitatsverlust schon in einem
massigen Zeitraume sich durch einen deutlichen Spannungsabfall
zu erkennen giebt, schliesslich muss er bequem transportabel sein.
Nach einigen Vorversuchen entschieden wir uns aus diesen
Griinden dafur, als Messinstrument das so leicht zu handhabende
Exnersche Electroscop zu verwenden, indem wir daran einige Ab-
1 Die Beschreibung des Apparats ist mit einigen Zusatzen aus der Physikalischcn
Zeiischrift 1899, p. 11 entnommen.
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ELECIRISCHE I ON EN IN DER ATMOSPHERE
217
anderungen anbrachten, die neben einef wesentlichen Verbesse-
rung der Isolation den Zweck hatten, die zu diesen Messungen no-
tigen verschiedenen Operationen in einheitlicher Weise zu ver-
binden.
I igur I
Die etwas stark gearbeitete Trennungsplatte A Fig. I der Alu-
miniumblattchen tragt an ihrem unteren Ende einen kurzen cylin-
dierten Ansatz A' aus Messing und ist mit diesem, abweichend von
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218 /. ELSTER UND H. GEITEL [Vol. iv,no. 4 ]
der Exnerschen Construction, an der tiefsten Stelle des Gehauses
in einen starken gefirnissten Ebonitstopfen eingelassen. Oben en-
det sie in eine kleine Kugel B mit conischer Bohrung c. Liegt das
Instrument in dem zugehorigen Etui, so ist das Gehause oben durch
den Deckel D geschlossen und die Schutzbacken E sind zusammen-
geschoben. Vor dem Gebrauche nimmt man den Deckel ab, zieht
die Schutzbacken zuriick, soweit dies moglich ist und fiihrt durch
die Oeffnung F des Gehauses einen Metallstift ein, dessen unteres
conisches Ende genau in die Bohrung der Kugel B hineinpasst.
Handelt es sich um die Benutzung des Instruments zu Messungen
von Potentialdifferenzen, so muss dieser Stift an seinem oberen aus
F hervorragenden Ende eine Klemmschraube zur Herstellung von
Drahtverbindungen tragen, soil es zu Zerstreuungsbeobachtungen
dienen, so ist dem Stifteein geschlossener cylindrischer Hohlkorper
G aus geschwarztem Messingblech von 9 cm. Hohe und 5 c;n.
Durchmesser aufgesetzt. (Anfangs verwandten wir statt dessen
einen Korper von denselben Dimensionen aus Zinkblech, den wir
mit Papier iiberklebten. Wir wollten auf diese Weise den Fehler
vermeiden, der bei Metallflachen durch photoelectrische Wirkun-
gen verursacht werden kann, iiberzeugten uns aber, dass auch das
geschwarzte Messing zu keinerlei Bedenken Anlass giebt und dabei
unveranderlicher ist, als eine Papierflache.)
Der Vorzug der beschriebenen Konstruction des Electroskopes
liegt darin, dass die einzige isolierende Vorrichtung weder mit der
Aussenluft noch irgend welchen fremden Korpern in Beriihrung
kommen kann. Will man sie noch gegen einfallenden Staub und
gegen Licht schiitzen, so ist dies durch eine unmittelbar iiber dem
Ebonit bei A ' angebrachte Schutzplatte aus diinnem Messingblech
leicht erreichbar.
Fur den Fall, dass bei hohem Feuchtigkeitsgehalte der Luft die
Isolation mangelhaft wird, ist eine Trockenkammer angebracht,
namlich der fur gewohnlich durch einen Gummistopfen geschlos-
sene Glastubus /f, in den ein erbsengrosses Stiick metallischen
Natriums, an eine durch einen Gummistopfen gefuhrte Nadel auf-
gespiesst, eingebracht werden kann. Selbstverstandlich muss das
Natrium, bevor der Apparat nach dem Gebrauche in das Etui ge-
legt wird, entfernt werden. Zur Aufbewahrung dient ein kleines
Glasrohrchen von denselben Dimensionen wie der Tubus H. Pet-
roleum u. dgl. zur Conservierung des Metalls wird nicht verwandt ;
eine starke Schicht von Oxyd ist fur die austrocknende Wirkung
kein Hinderniss.
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ELECTRISCHE I ON EN IN DER A TMOSPH&RE 2 1 9
Skala und Visierstreif sind wie bei der urspriinglichen Form
angebracht, die Aichung des Instruments geschieht am einfachsten
an einem Hochspannungsaccumulator.
Zur Anstellung von Zerstreuungsversuchen in geschlossenen
Raumen setzt man das Electroscop auf den in der Mitte eines von
Stellschrauben getragenen Dreifusses befestigten Zapfen /, fiihrt den
Zerstreuungskorper G ein und ladet dann das aus diesem und dem
Electroscope zusammengesetzte System mittelst einer Zambonischen
Saule etwa positiv. Man wartet nun ungef ahr 5', damit der isolie-
rende Ebonitstopfen an der Beruhrungslinie seiner Oberflache mit
dem eingefiigten Metallcylinder sich positiv laden und innen dielec-
trisch polarisieren konne und liest dann die Divergenz der Blatt-
chen ab; dieser moge nach der Aichungstabelle ein Potential von
Vo Volt entsprechen.
Je nach dem Grade der Zerstreuung iiberlasst man nun den Ap-
parat kiirzere oder langere Zeit (bis 15') sich selbst, bis eine deut-
liche Spannungsabnahme stattgefunden hat, liest dann wieder die
Divergenz ab (entsprechend V Volt) und notiert die zwischen bei-
den Ablesungen liegende Zeit /. Alsdann entfernt man den Zer.
streuungscylinder G und fiihrt statt dessen einen mit isolierender
Handhabe versehenen Stift K ein, ladet nochmals mit demselben
Vorzeichen, zieht den Stift heraus, so dass jetzt die Electroscop-
blattchen mit ihrem Trager electrisiert zuriickbleiben und beobach-
tet wiederum ihre Divergenz ( JV). Nach der Zeit /', mindestens
derselben, die man auf den ersten Versuch verwandt hatte, liest
man die Divergenz V ab. Wahrend dieser Zeit bleibt das Ge-
hause des Electrocops offen. Bezeichnet man nun mit n das Ver-
haltnis der Capacitaten des Electroscops allein zu der Summe der
Capacitaten vom Electroscop und Zerstreuungscylinder, so ist der
Ausdruck :
^ / . Vo n f Vo'
E= T \og v - 7r logy,
ein Maass fur die wahrend der Expositionszeit von dem Zerstreu-
ungscylinder einschliesslich des ihn tragenden Stiftes an die Luft
abgegebene Electricitatsmenge.
Will man einen Versuch mit negativer Ladung anschliessen,.
so muss man vor der ersten Able 
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